a new value picking regularization strategy application to the 3 d electromagnetic inverse scattering problem the nonlinear electromagnetic inverse scattering problem of reconstructing a possibly quasi piecewise constant inhomogeneous complex permittivity profile is solved by iterative minimization of a pixel based data fit cost function because of the ill posedness it is necessary to introduce some form of regularization many authors apply a smoothing constraint on the reconstructed permittivity profile but such regularization smooths away sharp edges in this paper a simple yet effective regularization strategy the value picking vp regularization is proposed this new technique is capable of reconstructing piecewise constant permittivity profiles without degrading the edges it is based on the knowledge that only a few different permittivity values occur in such profiles the values of which need not be known in advance vp regularization does not impose this a priori information in a strict sense such that it can be applied also to profiles that are only approximately piecewise constant the vp regularization is introduced in the solution of the inverse problem by adding a choice function to the data fit cost function for every permittivity unknown in the discretized problem when minimized the choice function forces the corresponding permittivity unknown to be close to one member of a set of auxiliary variables the vp values which are continuously updated throughout the iterations to minimize the regularized cost function a half quadratic gauss newton optimization technique is presented finally a stepwise relaxed vp regularization scheme is proposed in which the number of vp values is gradually increased this scheme is tested with synthetic and measured scattering data obtained from inhomogeneous 3d targets and is shown to achieve high reconstruction quality

alternating adaptive projections in antenna synthesis the projection operator is a basic building block in the application of the alternating projections method to antenna synthesis in general it is a non linear operator that is repeatedly applied in the course of a single synthesis process thus having a considerable impact on the convergence properties of the resulting algorithm a novel approach to the computation of these projections is presented which exploits a simple definition of the relevant spaces particularly that of radiated fields characterization of field mask specification as scale invariant under this definition adds a further degree of freedom namely reference level which impacts on the sensitive to scaling projector in order to compute the optimum reference level an iterative procedure is proposed which is simple to implement easily integrable in standard alternating projection routines and adds negligible computational burden numerical tests confirm an improved performance with respect to the fixed scaling projection operator in terms of convergence rate and robustness against the initial guess supporting our approach as a valid aid in overcoming the drawbacks of the alternating projections based antenna synthesis

preservation of prox regularity of sets with applications to constrained optimization in this paper we first provide counterexamples showing that sublevels of prox regular functions and levels of differentiable mappings with lipschitz derivatives may fail to be prox regular then we prove the uniform prox regularity of such sets under usual verifiable qualification conditions the preservation of uniform prox regularity of intersection and inverse image under usual qualification conditions is also established applications to constrained optimization problems are given

determining surface temperatures from interior observations we consider the inverse heat transfer problem for the case of the one dimensional heat equation in a quarter plane and present a new solution algorithm together with error bounds of logarithmic convexity type our method is based on regularizing the initial value problem for the heat equation run sideways we describe a numerical experiment with rapidly varying temperature profiles and explain how the method can be extended to problems with temperature dependent thermal properties

optimal far field focusing of uniformly spaced arrays subject to arbitrary upper bounds in nontarget directions a new approach providing new theoretical results to the optimal far field focusing of uniformly spaced arrays subject to a completely arbitrary mask for sidelobe bounds is presented and discussed in both cases of linear or planar arrays with rectangular boundaries it is first shown that the problem can be formulated without any loss to performances on the maximum as a linear programming one guaranteeing a globally optimal solution second a sufficient uniqueness criterion for the solution of the overall problem is also developed which shows how the solution may not be unique as is actually the case when planar arrays are considered in addition further globally effective optimization procedures are proposed for the latter case in order to optimize directivity smoothness of excitations or other performance parameters in the set of equivalent solutions last an extension to planar arrays with a nonrectangular boundary is also given a thorough numerical analysis confirms the effectiveness of the approach proposed and of the solution codes developed

invariant sets and lyapunov pairs for differential inclusions with maximal monotone operators we give different conditions for the invariance of closed sets with respect to differential inclusions governed by a maximal monotone operator defined on hilbert spaces which is subject to a lipschitz continuous perturbation depending on the state these sets are not necessarily weakly closed as in 3 4 while the invariance criteria are still written by using only the data of the system so no need to the explicit knowledge of neither the solution of this differential inclusion nor the semi group generated by the maximal monotone operator these invariant viability results are next applied to derive explicit criteria for a lyapunov pairs of lower semi continuous not necessarily weakly lsc functions associated to these differential inclusions the lack of differentiability of the candidate lyapunov functions and the consideration of general invariant sets possibly not convex or smooth are carried out by using techniques from nonsmooth analysis

a complete set of linear phase basis functions for scatterers with flat faces and for planar apertures entire domain basis functions are introduced for the analysis of scattering from bodies with flat portions and of radiation from planar apertures they are defined via the application of the sampling theorem of shannon these basis functions are particularly convenient for polygonal contours however arbitrary contours can be treated in the same framework with a very minor pre processing time a non redundant set of basis functions is determined a priori by explicit approximate formulas either for currents and for radiated field numerical results are presented to shown the accuracy of the method

on the sampling of the electromagnetic field radiated by sparse sources the aim of this paper is to discuss the effectiveness of random sampling of the electromagnetic field in problems involving sparse radiating sources the method adopted in this paper uses an intuitive geometrical approach based on the johnson linderstrauss lemma applied to the epsilon net of the set of the fields radiated by the sparse source the paper shows that a proper non uniform random sampling nurs using some a priori information on the problem allows a significant reduction in the cardinality of the set of the measured data compared to uniform random sampling and to random sampling from a lambda 2 equispaced set of data it is also shown that there is a limiting number of data after which random sampling is not convenient in this case a deterministic sampling strategy called modified non uniform sampling mnus is proposed numerical results on linear sparse arrays confirm the effectiveness of nurs and mnus

on the role of the number of degrees of freedom of the field in mimo channels the aim of this paper is to investigate the relationship between the effective number of degrees of freedom endf of a multiple input multiple output mimo channel and the number of degrees of freedom ndf of the field in particular the ndf of the field represents an upperbound for the endf of a mimo channel consequently the evaluation of the maximum endf can be carried out by adopting the literature on the ndf based on the spatial bandlimitation properties of the field this approach allows a simple and intuitive explanation of the maximum endf in a mimo channel based on a geometrical interpretation of the spatial channel in terms of spatial nyquist intervals

arnoldi tikhonov regularization methods tikhonov regularization for large scale linear ill posed problems is commonly implemented by determining a partial lanczos bidiagonalization of the matrix of the given system of equations this paper explores the possibility of instead computing a partial arnoldi decomposition of the given matrix computed examples illustrate that this approach may require fewer matrix vector product evaluations and therefore less arithmetic work moreover the proposed range restricted arnoldi tikhonov regularization method does not require the adjoint matrix and hence is convenient to use for problems for which the adjoint is difficult to evaluate

an efficient algorithm for regularization of laplace transform inversion in real case we address design of a numerical algorithm for solving the linear system arising in numerical inversion of laplace transforms in real case l d amore a murli regularization of a fourier series method for the laplace transform inversion with real data inverse problems 18 2002 1185 1205 the matrix has a condition number that grows almost exponentially and the singular values decay gradually towards zero in such a case because of this intrinsic strong instability the main difficulty of any numerical computation is the ability of discovering at run time only using data what is the maximum attainable accuracy on the solution in this paper we use gmres with the aim of relating the current residuals to the maximum attainable accuracy of the approximate solution by using a suitable stopping rule we prove that gmres stops after at most as many iterations as the number of the largest eigenvalues compared to the machine epsilon we use a split preconditioner that symmetrically precondition the initial system by this way the largest eigenvalue dynamically provides the estimate of the condition number of the matrix

the θ exterior sphere condition φ convexity and local semiconcavity abstract we consider sets s r n satisfying a locally uniform exterior sphere condition called the exterior sphere condition it is shown that under wedgedness of s this coincides with the convexity property studied by colombo and marigonda 2005 5 this generalizes and improves upon the main result of nour et al 2009 10 where the constant radius case was considered we also generalize certain known results concerning the regularity of the distance function associated with s as well as semiconcavity and other properties of functions with hypographs satisfying the exterior sphere condition

mixed semicontinuous perturbations of nonconvex sweeping processes in this paper we prove a theorem on the existence of a global solution of a differential inclusion governed by a class of nonconvex sweeping processes with unbounded pertubations the perturbations are not required to be convex valued

weak regularity of functions and sets in asplund spaces abstract in this paper we study a new concept of weak regularity of functions and sets in asplund spaces we show that this notion includes prox regular functions functions whose subdifferential is weakly submonotone and amenable functions in infinite dimension we establish also that weak regularity is equivalent to mordukhovich regularity in finite dimension finally we give characterizations of the weak regularity of epi lipschitzian sets in terms of their local representations

on the structure of the minimum time function a minimum time problem with a nonlinear smooth dynamics and a target satisfying an internal sphere condition is considered under the assumption that the minimum time t be continuous and the normal cone to the hypograph of t n hypo t be pointed we show that hypo t is varphi convex i e satisfies a strong external sphere condition consequently t is a e twice differentiable and satisfies some further regularity properties our results are based on a representation of clarke generalized gradient of t an example is provided showing that if n hypo t is not pointed then the result may fail

some new regularity properties for the minimal time function a minimal time problem with linear dynamics and convex target is considered it is shown essentially that the epigraph of the minimal time function t cdot is varphi convex i e it satisfies a kind of exterior sphere condition with locally uniform radius provided t cdot is continuous several regularity properties are derived from results in g colombo and a marigonda calc var partial differential equations 25 2005 pp 1 31 including twice a e differentiability of t cdot and local estimates on the total variation of dt

on electromagnetics and information theory some connections are described between electromagnetic theory and information theory identifying some unavoidable limitations imposed by the laws of electromagnetism to communication systems starting from this result the role of the degrees of freedom of the field in radiating systems is investigated different classes of antennas use the available degrees of freedom in different ways in particular a multiple input multiple output antenna is a radiating system conveying statistically independent information on more than one degree of freedom of the field applications of the theory to antenna synthesis and antenna characterization in complex environments are shown

a new formulation for the radiation operator application to the fast computation of the singular value decomposition this paper proposes a new formula for the operator mathcal k given by the product of the radiation operator by its adjoint the formula expresses mathcal k by means of a surface integral extended to the boundary of the source domain rather than a volume integral extended to the whole source domain as entailed by its mathematical definition as a result the computation of mathcal k becomes much less onerous than the computation based on its mathematical definition an immediate application of the derived formula is the fast computation of the singular value decomposition of the radiation operator through to the fast computation of mathcal k some possible implications of the derived formula for mathcal k are also discussed finally numerical examples are provided as proof of the validity and effectiveness of the formula

existence and differentiability of metric projections in hilbert spaces this paper considers metric projections onto a closed subset s of a hilbert space if the set s is convex then it is well known that the corresponding metric projections always exist unique and directionally differentiable at boundary points of s these properties of metric projections are considered for possibly nonconvex sets s in particular existence and directional differentiability of metric projections for certain classes of sets are established and will be referred to as nearly convex sets

optimal interpolation of radiated fields over a sphere an optimal sampling interpolation algorithm is developed that allows the accurate recovery of scattered or radiated fields over a sphere from a minimum number of samples using the concept of the field equivalent spatial bandwidth a central interpolation scheme is developed to compute the field in theta phi coordinates starting from its samples the maximum allowable sample spacing and error upper bounds are also rigorously derived several simulated examples of pattern reconstruction are presented for both the cases of field and power pattern interpolation the interpolation error as a function of the retained sample number has been also evaluated and compared with the theoretical upper bounds the algorithm stability versus randomly distributed errors added to the exact samples is demonstrated

multiscale compressed block decomposition for fast direct solution of method of moments linear system the multiscale compressed block decomposition algorithm ms cbd is presented for highly accelerated direct non iterative solution of electromagnetic scattering and radiation problems with the method of moments mom the algorithm is demonstrated to exhibit n2 computational complexity and storage requirements scaling with n1 5 for electrically large objects several numerical examples illustrate the efficiency of the method in particular for problems with multiple excitation vectors the largest problem presented in this paper is the monostatic rcs of the nasa almond at 50 ghz for one thousand incidence angles discretized using 442 089 rwg basis functions being entirely algebraic ms cbd is independent of the greens function of the problem

efficient near field far field transformation for nonredundant sampling representation on arbitrary surfaces in near field antenna measurements a nonredundant sampling representation on arbitrary surfaces in near field antenna measurements together with a direct near field far field transformation is described the utilized sampling criterion depends on the electrical size of the antenna under test aut along with the separation between the aut and the measurement surface the minimum number of samples required is directly linked with the number of unknowns in the linear system of equations derived considering spherical expansion of radiated aut fields equivalent plane wave sources are used to represent the aut fields plane wave translations can be directly performed for any arbitrary measurement grid with the same efficiency thus nonredundant sampling representations can be utilized on any scan surface in contrast other fast field transformation techniques would lose their efficiency the proposed sampling is applied to near field measurements and synthetic data using a variety of antennas and the results are compared to the case of standard sampling remarkable decrease in the number of measurement points is observed with a negligible change in the accuracy of the transformed pattern thereby greatly reducing the measurement time and the computational effort

physical optics analysis of multiple interactions in large scatters using current modes an efficient scheme based on physical optics po to analyze the mutual interactions between the parts of large bodies is presented the po current is approximated by current modes defined as complex exponential functions both the body geometry and the current modes are represented by means of nonuniform rational bi spline surfaces functions the current modes are computed by extrapolation considering the current values in a set of sampling points a new interpolation scheme to obtain the phase of the current modes using samples of the spatial frequency is presented the field due to the current modes is calculated efficiently using analytical expressions some results are also presented that show the performances of the method

the proximal normal formula in banach space approximation by proximal normals to the clarke generalized subdifferential for a distance function generated by a nonempty closed set and the normal cone to the set generated by the proximal normals are important tools in nonsmooth analysis we give simple general versions of such formulae in infinite dimensional banach spaces which satisfy different geometrical conditions our first class of spaces with uniformly g teaux differentiable norm includes the hilbert space case and the formulae is attained through dense subsets our second class of reflexive kadec smooth spaces is the most general for which such formulae can be obtained for all nonempty closed sets in the space our technique also allows us to establish the existence of solutions for a class of optimization problems substantially extending similar work of ekeland and lebourg

krylov subspace iterative methods for boundary element method based near field acoustic holography the reconstruction of the acoustic field for general surfaces is obtained from the solution of a matrix system that results from a boundary integral equation discretized using boundary element methods the solution to the resultant matrix system is obtained using iterative regularization methods that counteract the effect of noise on the measurements these methods will not require the calculation of the singular value decomposition which can be expensive when the matrix system is considerably large krylov subspace methods are iterative methods that have the phenomena known as semi convergence i e the optimal regularization solution is obtained after a few iterations if the iteration is not stopped the method converges to a solution that generally is totally corrupted by errors on the measurements for these methods the number of iterations play the role of the regularization parameter we will focus our attention to the study of the regularizing properties from the krylov subspace methods like conjugate gradients least squares qr and the recently proposed hybrid method a discussion and comparison of the available stopping rules will be included a vibrating plate is considered as an example to validate our results

representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples it is shown that the electromagnetic em field radiated or scattered by bounded sources can be accurately represented over a substantially arbitrary surface by a finite number of samples even when the observation domain is unbounded the number of required samples is nonredundant and essentially coincident with the number of degrees of freedom of the field this result relies on the extraction of a proper phase factor from the field expression and on the use of appropriate coordinates to parameterize the domain it is demonstrated that the number of degrees of freedom is independent of the observation domain and depends only on the source geometry the case of spheroidal sources and observation domains with rotational symmetry is analyzed in detail and the particular cases of spherical and planar sources are explicitly considered for these geometries precise and fast sampling algorithms of central type are presented which allow an efficient recovery of em fields from a nonredundant finite number of samples such algorithms are stable with respect to random errors affecting the data

phaseless antenna measurement on non redundant sample points via leith upatnieks holography a scheme for reducing the number of sample points in phaseless acquisition based on leith upatnieks holography is presented an appropriate choice of the phase of the reference field enables to drastically decrease the sampling rate by acquiring the so called reduced field instead of the real radiated field the reference phase changes are enabled by applying the recent developments on the synthesis of the reference wave moreover optimal sampling interpolation can be applied to the retrieved field so that the real field can be computed at any point on the acquisition surface the method is illustrated by means of multiple simulations for observation domains such as straight lines azimuthal circles as well as for a plane polar acquisition scheme

comments on fast direct solution of method of moments linear system in the above named work a new algorithm is presented for direct non iterative frequency domain method of moments mom calculations based on block wise compression of the impedance matrix the storage requirements and computational complexity of the algorithm are claimed to be n3 2 and n2 respectively if n is the number of unknowns for a mom surface discretization that is fixed with respect to the wavelength a more rigorous analysis explicitly using the asymptotic expression for the number of degrees of freedom dof in the interaction between groups of scatterers is presented here showing that this should be n3 2log n and n2log2 n respectively the complexity analysis applies to problems that can be formulated as a surface integral equation sie on surfaces in or between homogeneous media such as a ship or an airplane it does not apply to volume discretization mom or multilayer problems the results presented here are also relevant for block wise compression methods using iterative solvers since the compressed impedance matrix is the same consequently the above complexity analysis applies to very large problems well beyond the reach of even the largest existent computers for moderate size problems the measured complexity is lower

an effective deterministic procedure for the synthesis of shaped beams by means of uniform amplitude linear sparse arrays a rigorous deterministic approach is proposed for the mask constrained power pattern synthesis of shaped beams through one dimensional sparse arrays having uniform amplitude excitations and variable phases the approach includes the well known density taper procedure as a special case the corresponding technique which exploits an analytical formulation of the problem and convex programming routines results in fast computation and is able to achieve optimal solutions without recurring to any global optimization numerical results assessing the capabilities of the proposed design method are provided opening the way to the development of an effective approach for the synthesis of circularly symmetric shaped beams via uniformly excited circular ring arrays

some properties of range restricted gmres methods the gmres method is one of the most popular iterative schemes for the solution of large linear systems of equations with a square nonsingular matrix gmres type methods also have been applied to the solution of linear discrete ill posed problems computational experience indicates that for the latter problems variants of the standard gmres method that require the solution to live in the range of a positive power of the matrix of the linear system of equations to be solved generally yield more accurate approximations of the desired solution than standard gmres this paper investigates properties of these variants of gmres

sweeping by a continuous prox regular set abstract the evolution problem known as sweeping process is considered for a class of nonconvex sets called prox regular or convex assuming essentially that such sets contain in the interior a suitable subset and move continuously w r t the hausdorff distance we prove local and global existence as well as uniqueness of solutions which are continuous functions with bounded variation some examples are presented

gmres type methods for inconsistent systems abstract the behavior of iterative methods of gmres type when applied to singular possibly inconsistent linear systems is discussed and conditions under which these methods converge to the least squares solution of minimal norm are presented error bounds for the computed iterates are shown this paper complements previous work by brown and walker p n brown h f walker siam j matrix anal appl 18 1997 37 51

fast antenna diagnosis algorithm using oblate spheroidal nonuniform grids a fast algorithm for the diagnosis of large antennas is developed the algorithm is based on the rayleigh sommerfeld rs backpropagation method accelerated by a multilevel nonuniform grid algorithm comparison between the field distributions reconstructed from measurements and the desired ones can be used for the localization of antenna defects and geometrical distortions the optimal performance is obtained by using oblate spheroidal grids which are tailored to both the measurement and antenna surfaces further acceleration can be achieved for particular cases via optimal sampling on the antenna surface the algorithm s performance is demonstrated for the example of a parabolic reflector with a number of surface distortions and compared to that achieved with spherical grids the accuracy and error controllability are studied in comparison to the direct rs integral computation

a new method for avoiding the truncation error in near field antennas measurements a new method to avoid the truncation error in antenna near field measurements is presented the approach relies on the concept of information content of the field according to this point of view the truncation problem is solved by picking up the information that is lost due to the finite size of scanning area in points of the space reachable by the measurement system the method can be applied to any scanning geometry including the planar and cylindrical ones whenever the set up allows to vary the distance between the antenna under test and the probe during the scanning procedure application of the method to cylindrical near field scanning is numerically investigated assessing the effectiveness of the proposed technique

exterior sphere condition and time optimal control for differential inclusions the minimum time function t cdot of smooth control systems is known to be locally semiconcave provided petrov s controllability condition is satisfied moreover such a regularity holds up to the boundary of the target under an inner ball assumption we generalize this analysis to differential inclusions replacing the above hypotheses with the continuity of t cdot near the target and an inner ball property for the multifunction associated with the dynamics in such a weakened setup we prove that the hypograph of t cdot satisfies locally an exterior sphere condition as is well known this geometric property ensures most of the regularity results that hold for semiconcave functions without assuming t cdot to be lipschitz

an extension of attouch s theorem and its application to second order epi differentiation of convexly composite functions in 1977 hedy attouch established that a sequence of closed proper convex functions epi converges to a convex function if and only if the graphs of the subdierentials converge in the mosco sense to the subdifferential of the limiting function and roughly speaking there is a condition that fixes the constant of integration we show that the theorem is valid if instead one considers functions that are the composition of a closed proper convex function with a twice continuously differentiable mapping in addition a constraint qualification is imposed

local differentiability of distance functions recently clarke stern and wolenski characterized in a hilbert space the closed subsets c for which the distance function dc is continuously differentiable everywhere on an open tube of uniform thickness around c here a corresponding local theory is developed for the property of dc being continuously differentiable outside of c on some neighborhood of a point x c this is shown to be equivalent to the prox regularity of c at x which is a condition on normal vectors that is commonly fulfilled in variational analysis and has the advantage of being verifiable by calculation additional characterizations are provided in terms of dc being locally of class c 1 or such that dc 2 is convex around x for some 0 prox regularity of c at x corresponds further to the normal cone mapping nc having a hypomonotone truncation around x and leads to a formula for pc by way of nc the local theory also yields new insights on the global level of the clarke stern wolenski results and on a property of sets introduced by shapiro as well as on the concept of sets with positive reach considered by federer in the finite dimensional setting

on landau s eigenvalue theorem and information cut sets a variation of landau s eigenvalue theorem describing the phase transition of the eigenvalues of a time frequency limiting self adjoint operator is presented the total number of degrees of freedom of square integrable multidimensional bandlimited functions is defined in terms of kolmogorov s n width and computed in some limiting regimes where the original theorem cannot be directly applied results are used to characterize up to order the total amount of information that can be transported in time and space by multiple scattered electromagnetic waves rigorously addressing a question originally posed in the early works of toraldo di francia and gabor applications in the context of wireless communication and electromagnetic sensing are discussed

optimal synthesis of circularly symmetric shaped beams the problem of the optimal power pattern synthesis of circularly symmetric shaped beams is addressed and solved in particular an existence criterion is provided to test a priori i e without solving the overall synthesis problem if a non superdirective source of given size can radiate or not a circularly symmetric power pattern lying in a given arbitrary mask in the affirmative case the proposed approach guarantees the achievement of the optimal solution i e that of maximum directivity or minimum size by using convex optimization techniques in general a number of equivalent source distributions i e radiating the same power pattern do exist which can be explicitly determined in a deterministic way numerical examples concerning applications of actual interest support the given theory and confirm the effectiveness of the developed synthesis procedure

on the regularizing properties of the gmres method the gmres method is a popular iterative method for the solution of large linear systems of equations with a nonsymmetric nonsingular matrix however little is known about the behavior of this method when it is applied to the solution of nonsymmetric linear ill posed problems with a right hand side that is contaminated by errors we show that when the associated error free right hand side lies in a finite dimensional krylov subspace the gmres method is a regularization method the iterations are terminated by a stopping rule based on the discrepancy principle

a modified tikhonov regularization method tikhonov regularization and truncated singular value decomposition tsvd are two elementary techniques for solving a least squares problem from a linear discrete ill posed problem based on these two techniques a modified regularization method is proposed which is applied to an arnoldi based hybrid method theoretical analysis and numerical examples are presented to illustrate the effectiveness of the method

fast and accurate near field far field transformation by sampling interpolation of plane polar measurements an optimal sampling interpolation algorithm which allows the accurate recovery of plane rectangular near field samples from the knowledge of the plane polar ones is developed this enables the standard near field far field nf ff transformation which takes full advantage of the fast fourier transform fft algorithm to be applied to plane polar scanning the maximum allowable sample spacing is also rigorously derived and it is shown that it can be significantly greater than lambda 2 as the measurement place moves away from the source this allows a remarkable reduction of both measurement time and memory storage requirements the sampling approach is compared with that based on the bivariate lagrange interpolation bli method the sampling reconstruction agrees with the exact results significantly better than the bli in spite of the significantly lower number of required measurements

solving an ill posed cauchy problem for a two dimensional parabolic pde with variable coefficients using a preconditioned gmres method the sideways parabolic equation spe is a model of the problem of determining the temperature on the surface of a body from the interior measurements mathematically it can be formulated as a noncharacteristic cauchy problem for a parabolic partial differential equation this problem is severely ill posed in an l 2 setting we use a preconditioned generalized minimum residual method gmres to solve a two dimensional spe with variable coefficients the preconditioner is singular and chosen in a way that allows efficient implementation using the fft the preconditioner is a stabilized solver for a nearby problem with constant coefficients and it reduces the number of iterations in the gmres algorithm significantly numerical experiments are performed that demonstrate the performance of the proposed method

hypographs satisfying an external sphere condition and the regularity of the minimum time function abstract we prove that if the hypograph of a continuous function f admits at every boundary point a supporting ball then it has essentially positive reach i e the hypograph of the restriction of f outside a closed set of zero measure has locally positive reach hence such a function enjoys some properties of a concave function in particular a e twice differentiability we apply this result to a minimum time problem in the case of a nonlinear smooth dynamics and a target satisfying internal sphere condition

improvement of space invariant image deblurring by preconditioned landweber iterations the landweber method is a simple and flexible iterative regularization algorithm whose projected variant provides nonnegative image reconstructions since the method is usually very slow we apply circulant preconditioners exploiting the shift invariance of many deblurring problems in order to accelerate the convergence this way reasonable reconstructions can be obtained within a few iterations the method becomes competitive and more robust than other approaches that although faster sometimes lead to lower accuracy some theoretical analysis of convergence is given together with numerical validations

controllability of some nonlinear systems with drift via generalized curvature properties we discuss the problem of local attainability for finite dimensional nonlinear control systems with quite general assumptions on the target set special emphasis is given to control affine systems with a possibly nontrivial drift term to this end we provide some sufficient conditions ensuring local attainability which involve geometric properties both of the target itself such as a notion of generalized curvature and of the lie algebra associated with the control system the main technique used is a convenient representation formula for the power expansion of the distance function along the trajectories made at points sufficiently near to the target set

the degrees of freedom of wireless networksvia cut set integrals the problem of determining the number of spatial degrees of freedom d o f of the signals carrying information in a wireless network is reduced to the computation of the geometric variation of the environment with respect to the cut through which the information must flow physically this has an appealing interpretation in terms of the diversity induced on the cut by the possible richness of the scattering environment mathematically this variation is expressed as an integral along the cut which we call cut set integral and whose scaling order is evaluated exactly in the case of planar networks embedded in arbitrary three dimensional 3 d environments presented results shed some new light on the problem of computing the capacity of wireless networks showing a fundamental limitation imposed by the size of the cut through which the information must flow in an attempt to remove what may appear as apparent inconsistencies with previous literature we also discuss how our upper bounds relate to corresponding lower bounds obtained using the techniques of multihop hierarchical cooperation and interference alignment

minimum trace norm regularization mtnr in electromagnetic inverse problems this paper discusses a method to regularize linear problems in presence of incomplete and noisy data generated by partially or totally unknown sources the idea is to identify the simplest solution looking for the system having the minimum number of degrees of freedom ndf compatible with the available data it is shown that a normalized version of the trace norm known as 1 schatten norm in functional analysis is a good convex approximation of the ndf of the field this allows to use the trace norm as a convex surrogate of the ndf in the minimization process taking advantage of the recent literature on rank minimization examples regarding mimo beamforming from incomplete channel matrix field interpolation with no a priori information on the sources and land mine identification using the total field are discussed

the sub cauchy stokes problem solvability issues and lagrange multiplier methods with artificial boundary conditions in contrast to the conventional cauchy stokes problems in which the velocity and the stress force data are given on the accessible boundary in the present paper we reduce the accessible boundary data information and we consider a problem which deals only with shear stress data we refer to this problem as a sub cauchy stokes problem this problem is ill posed because of severe instability and even uniqueness is unknown we first address the uniqueness issues associated with this problem resorting to the domain decomposition techniques together with the duplication process of vogelius 1 we propose new lagrange multiplier methods to solve the sub cauchy stokes problem these methods consist in recasting the problem in terms of interfacial equations by equalizing two solutions of the sub cauchy stokes problem using matching conditions defined on the inaccessible boundary the matching is based on second order conditions and depends on the equations used to match the values of the unknowns on the inaccessible boundary the underlying interfacial problems are then solved by iterative procedures in which coefficients can be optimized to improve convergence rates a complete analysis of the methods is presented and various numerical results illustrate the effectiveness and the performance of the proposed approaches

efficient algorithm for the evaluation of the physical optics scattering by nurbs surfaces with relatively general boundary condition an adaptive integration algorithm is presented for the computation of the physical optics po electric and magnetic field scattered by electrically large objects modeled by non uniform rational b splines nurbs the algorithm is the customization of a more general purpose result that has been recently published by using a unique formulation both impenetrable e g impedance surfaces coated conductors as well as transparent thin sheet materials e g thin dielectric panels or frequency selective surfaces are treated via their fresnel reflection and transmission coefficients the po radiation integral is evaluated over the nurbs parametric domain since most of the computer aided geometric design cagd tools are based on nurbs the proposed algorithm allows a straightforward electromagnetic analysis of the structures by exploiting the standard available geometrical description with no need of generating new geometrical models furthermore the proposed adaptive sampling requires a number of integration points that is found to be drastically smaller than that resulting from standard nyquist based sampling integration algorithms such reduction of the sampling points is achieved by resorting to high frequency technique concepts and allows a significant reduction of the cpu computational burden therefore the algorithm is efficient and particulary suitable for the electromagnetic characterization of real life electrically large objects

iterative algorithms for a new class of extended general nonconvex set valued variational inequalities abstract some new classes of extended general nonconvex set valued variational inequalities and the extended general wiener hopf inclusions are introduced by the projection technique equivalence between the extended general nonconvex set valued variational inequalities and the fixed point problems as well as the extended general nonconvex wiener hopf inclusions is proved then by using this equivalent formulation we discuss the existence of solutions of the extended general nonconvex set valued variational inequalities and construct some new perturbed finite step projection iterative algorithms with mixed errors for approximating the solutions of the extended general nonconvex set valued variational inequalities we also verify that the approximate solutions obtained by our algorithms converge to the solutions of the extended general nonconvex set valued variational inequalities the results presented in this paper extend and improve some known results from the literature

boundary conditions and multiple image re blurring the lbt case in this paper we are concerned with deblurring problems in the case of multiple images coming from the large binocular telescope an important example of telescope of interferometric type for this problem we are interested in checking the role of the boundary conditions in the quality of the reconstructed image in particular we will consider reflective and anti reflective boundary conditions and the re blurring idea the results of the proposed combinations are quite satisfactory when compared with classical dirichlet or periodic boundary conditions especially when increasing the number of images acquired by the lbt this behavior is confirmed by a wide numerical experimentation

electromagnetic field synthesis by hierarchical plane wave based field transformation an optimization based field synthesis approach is presented that employs a hierarchical plane wave based field transformation concept for efficient evaluation of the inverse problem forward operator irregular transmit antenna array configurations can be used to synthesize a target field distribution in an arbitrarily shaped test volume with full consideration of the antenna element radiation characteristics for this purpose a triangular mesh forms the test zone boundary surface on which rao wilton glisson rwg vector basis functions perform electric and magnetic field testing an iterative krylov subspace solver is employed to solve the ill posed inverse problem for the transmit antenna coefficients the effectiveness accuracy and efficiency of the proposed field synthesis algorithm are demonstrated for configurations with test zone extents of up to one hundred wavelengths moreover the approach is utilized for antenna measurements where antenna near fields are transformed into far fields

on an eigenvalue property relevant in correspondence analysis and related methods abstract in correspondence analysis as well as in related methods such as dual scaling and homogeneity analysis one encounters singular values of a matrix q d r 1 2 fd c 1 2 where f is an n p nonnegative data matrix and d r and d c are diagonal matrices implicitly defined by the equations d r 1 n f1 p and d c 1 p f 1 n 1 i denotes the summation vector of order i an important and often cited property of these singular values is that they lie in the 0 1 interval in this paper this property will first be examined in the context of the aforementioned mathematically equivalent statistical methods it will become apparent that for proving the property knowledge of the method at hand i e dual scaling correspondence analysis or homogeneity analysis is essential we shall then show by using the general matrix q that the result follows by elementary matrix algebra due to the nonnegativity of f and the scalings imposed by the diagonal matrices d r and d c

on the degrees of freedom of scattered fields starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities the degrees of freedom of the scattered field are introduced and then computed the degrees of freedom are shown to be practically equal to the nyquist number appropriate to the effective spatial bandwidth of the scattered field and to the extension of the observation domain accordingly a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error it is also shown that the field representation can be made in terms of field values and simple sampling functions provided that a marginal increase in the approximation error is tolerated the results not only completely justify the use of sampling interpolation for representing scattering fields but also demonstrate that such representation is practically an optimal one an algorithm for the reconstruction of scattered fields given the maximum allowed error is then produced

superoptimal approximation for unbounded symbols abstract the superoptimal frobenius approximation of toeplitz matrices is considered in connection with the case of unbounded symbols in particular we use the superoptimal approximation as preconditioner for the cg method when a fisher hartwig singularity is present in the symbol with special regard to systems coming from times series and financial applications a theoretical discussion concerning classical circulant preconditioners and a numerical comparison with the strang and with the optimal approximations are presented particularly with reference to the presence of noise

arnoldi methods for image deblurring with anti reflective boundary conditions image deblurring with anti reflective boundary conditions and a non symmetric point spread function is considered several iterative methods based on krylov subspace projections as well as arnoldi tikhonov regularization methods with reblurring right or left preconditioners are compared the aim of the preconditioner is not to accelerate the convergence but to improve the quality of the computed solution and to increase the robustness of the regularization method right preconditioning in conjunction with methods based on the arnoldi process are found to be robust and give high quality restorations in particular when the observed image is contaminated by motion blur our new method is much more effective than other approaches described in the literature such as range restricted arnoldi methods and the conjugate gradient method applied to the normal equations implemented with the reblurring approach

implementations of range restricted iterative methods for linear discrete ill posed problems abstract this paper is concerned with iterative solution methods for large linear systems of equations with a matrix of ill determined rank and an error contaminated right hand side the numerical solution is delicate because the matrix is very ill conditioned and may be singular it is natural to require that the computed iterates live in the range of the matrix when the latter is symmetric because then the iterates are orthogonal to the null space computational experience indicates that it can be beneficial to require that the iterates live in the range of the matrix also when the latter is nonsymmetric we discuss the design and implementation of iterative methods that determine iterates with this property new implementations that are particularly well suited for use with the discrepancy principle are described

inverse correspondence analysis in correspondence analysis ca rows and columns of a data matrix are depicted as points in low dimensional space the row and column profiles are approximated by minimizing the so called weighted chi squared distance between the original profiles and their approximations see for example theory and applications of correspondence analysis academic press new york 1984 in this paper we will study the inverse ca problem that is the possibilities for retrieving one or more data matrices from a low dimensional ca solution we will show that there exists a nonempty closed and bounded polyhedron of such matrices we also present two algorithms to find the vertices of the polyhedron an exact algorithm that finds all vertices and a heuristic approach for larger sized problems that will find some of the vertices a proof that the maximum of the pearson chi squared statistic is attained at one of the vertices is given in addition it is discussed how extra equality constraints on some elements of the data matrix can be imposed on the inverse ca problem as a special case we present a method for imposing integer restrictions on the data matrix as well the approach to inverse ca followed here is similar to the one employed by de leeuw and groenen j classification 14 1997 3 in their inverse multidimensional scaling problem

a novel approach to scatterers localization problem a new approach to find the number and locations of electromagnetic scatterers sources from one view one frequency field data is presented the case of scatterers sources with dimensions comparable to the wavelength is considered first in order to devise an effective technique a new relevant property of the electromagnetic field the point source spectral content is introduced and its relationship with both the sliding windowed fourier transform of the field and the local bandwidth function is discussed to enlighten its usefulness it is also shown that a footprint of the scattering system encoding information on its geometry can be easily extracted from the scattered field by exploiting this new property on this basis the new localization technique is introduced in order to restrict the search region the minimum circular envelope enclosing the scatterers is found by purposely introducing a new technique exploiting the effective bandwidth of the radiated field then the number and locations of scatterers is retrieved by using the field local quantitative feature previously introduced without the complexities of the full inverse problem as it is usually done by the traditional approaches in this way not only a simplified technique is obtained but also the ill posedness of the problem and the noise effects are significantly mitigated the effectiveness of the proposed technique and its overall performance with respect to a singular value decomposition based approach are proved by means of a numerical analysis

generalized hessian properties of regularized nonsmooth functions we take up the question of second order expansions for a class of functions of importance in optimization namely moreau envelope regularizations of nonsmooth functions f it is shown that when f is prox regular which includes convex functions and the extended real valued functions representing problems of nonlinear programming the many second order properties that can be formulated around the existence and stability of expansions of the envelopes of f or of their gradient mappings are linked by surprisingly extensive lists of equivalences with each other and with generalized differentiation properties of f itself this clarifies the circumstances conducive to developing computational methods based on envelope functions such as second order approximations in nonsmooth optimization and variants of the proximal point algorithm the results establish that generalized second order expansions of moreau envelopes at least can be counted on in most situations of interest in finite dimensional optimization

on the optimal synthesis of sum or difference patterns of centrosymmetric arrays under arbitrary sidelobe constraints this paper deals with the optimal synthesis of sum or difference patterns radiated by an array of fixed geometry the aim is to establish the most general class of arrays for which such synthesis can be reduced to a linear programming problem extending and completing previous results regarding uniformly spaced linear and planar arrays it is shown that such a class consists of the centrosymmetric arrays whose element patterns are either equal or hermitian symmetric with respect to the center of symmetry the optimal solutions are also hermitian symmetric and the corresponding patterns are real furthermore it is shown that the above class of arrays coincides with that of the arrays capable of radiating real patterns some numerical examples are provided to give an idea of the geometries and the synthesis problems to which the achieved result successfully applies and of the achievable computational advantage

retrieving a contingency table from a correspondence analysis solution abstract correspondence analysis ca is a dimension reduction technique for categorical data in particular ca is typically applied to a contingency matrix in order to visualize the relationships within and between the categories of the two variables as represented by its rows and columns the ca solution can be obtained by considering a singular value decomposition of the so called matrix of standardized residuals inverse correspondence analysis considers the problem of retrieving the data underlying a given low dimensional ca solution using the specific structure of the ca solutions as well as the characteristics of the original data we formulate the inverse ca problem in an integer linear programming context considering various conditions involving the dimensions of the original data matrix the number of observations the precision and dimensionality of the ca solution we show that by solving the integer linear programs the original data can be retrieved

on the spatial bandwidth of scattered fields it is shown that the scattered fields are almost space bandlimited functions the effective bandwidth w is introduced and evaluated for a very general scattering system as well as the error made using functions bandlimited to w w for representing the scattered field the effective bandwidth is very simply related to the maximum dimension of the scattering system the error drops to negligible values for modest increases of w compared to w in the case of large scatterers important consequences of the above general results are finally stressed

optimality conditions and regularity results for time optimal control problems with differential inclusions abstract we study the time optimal control problem with a general target s for a class of differential inclusions that satisfy mild smoothness and controllability assumptions in particular we do not require petrov s condition at the boundary of s consequently the minimum time function t fails to be locally lipschitz never mind semiconcave near s instead of such a regularity we use an exterior sphere condition for the hypograph of t to develop the analysis in this way we obtain dual arc inclusions which we apply to show the constancy of the hamiltonian along optimal trajectories and other optimality conditions in hamiltonian form we also prove an upper bound for the hausdorff measure of the set of all non lipschitz points of t which implies that the minimum time function is of special bounded variation sbv

on the interpolation of electromagnetic near field without prior knowledge of the radiating source a method is proposed to interpolate the electromagnetic near field when no information on the radiating source is available in the absence of a priori knowledge general properties of the electromagnetic field are exploited to estimate the field namely the minimum complexity of the field and the continuity of the first derivatives these properties are enforced by minimizing the nuclear norm and using the thin plate spline interpolation results respectively the proposed procedure is validated experimentally by interpolating the planar electrical near field radiated by three antennas the quality of the interpolation and its robustness to noise are investigated despite its simplicity the interpolation method is able to properly estimate the near field from a random coarse sampling of 2 lambda the quality of the near field interpolation is also confirmed by deriving the far field these promising results pave the way for the development of fast antenna measurement procedures

integration of subdifferentials of lower semicontinuous functions on banach spaces abstract this paper studies the lower semicontinuous functions on banach spaces whose subdifferentials are not disassociated from several conditions are given to ensure that two lower semicontinuous functions with the same subdifferential are equal up to an additive constant

integration of subdifferentials of nonconvex functions in nonsmooth analysis and optimization subgradients come in many different flavors e g approximate dini proximal clarke generalized see 2 5 6 12 14 191 these subgradients are important and valuable tools however many questions remain unsolved concerning the exact link between the function and its subgradients for instance can two functions not differing by an additive constant have the same subgradients in this paper we study the fundamental problem of determining functions that can be recovered up to an additive constant from the knowledge of their subgradients this integration problem is not very well understood and very few functions or classes of functions are known to be recoverable from their subgradients in section 4 we show that if the basic constraint qualification holds at r then the composition of a closed i e lowersemicontinuous proper convex function with a twice continuously differentiable mapping is determined up to an additive constant by its generalized subgradients actually in this case all above mentioned subgradients are the same beside the obvious theoretical interest of this integration problem it is our hope or perhaps our long term goal that once this problem is better understood we can then tackle the question of uniqueness of solutions to generalized differential equations involving subgradients in place of partial derivatives an example of such an equation that well deserves study is the extended hamilton jacobi equation used in optimal control see clarke 2 let us also mention that a problem similar to the integration problem is the one of determining the set valued mappings that are in fact subgradient set valued mappings uniqueness is not mandatory for a contribution to this problem see janin 8 before we look at some of the known cases where the function can be recovered from its subgradients let us look at some negative examples it is clear that not every function can be recovered up to an additive constant from its subgradients we only need to look at the following two functions 0 x50 0 x10 f x 1 x o g x 2 x o

preconditioned iterative methods for linear discrete ill posed problems from a bayesian inversion perspective in this paper we revisit the solution of ill posed problems by preconditioned iterative methods from a bayesian statistical inversion perspective after a brief review of the most popular krylov subspace iterative methods for the solution of linear discrete ill posed problems and some basic statistics results we analyze the statistical meaning of left and right preconditioners as well as projected restarted strategies computed examples illustrating the interplay between statistics and preconditioning are also presented

efficient sampling of electromagnetic fields via the adaptive cross approximation the adaptive cross approximation method is applied to the problem of efficiently sampling an electromagnetic field across two dimensions the algorithm uses previously collected samples to determine which field samples to take next and reduces the number of samples required to accurately represent the field in this way the field may be sampled faster than it would have been if it had been raster scanned this is achieved without significant changes to the sensor hardware

an effective nf ff transformation technique with planar spiral scanning tailored for quasi planar antennas an effective probe compensated near field far field transformation technique with planar spiral scanning is developed in this paper it makes use of an ellipsoidal modelling of the source instead of the previously adopted spherical one such a modelling tailored for quasi planar antennas allows one to consider measurement planes at a distance smaller than one half the antenna maximum size thus reducing the error related to the truncation of the scanning surface moreover it is quite general containing the spherical modelling as particular case and reduces significantly the number of the needed near field data when dealing with quasi planar antennas some numerical tests assessing the accuracy of the technique and its stability with respect to random errors affecting the data are reported

on p convex sets and geodesics on etudie les geodesiques sur une variete contrainte m a bord irregulier on considere une classe d ensembles irreguliers m qui permet d obtenir des resultats d existence et de multiplicite pour les geodesiques

partial extensions of attouch s theorem with applications to proto derivatives of subgradient mappings attouch s theorem which gives on a reflexive banach space the equivalence between the mosco epi convergence of a sequence of convex functions and the graph convergence of the associated sequence of subgradients has many important applications in convex optimization in particular generalized derivatives have been defined in terms of the epi convergence or graph convergence of certain difference quotient mappings and attouch s theorem has been used to relate these various generalized derivatives these relations can then be used to study the stability of the solution mapping associated with a parameterized family of optimization problems we prove in a hilbert space several partial extensions of attouch s theorem to functions more general than convex these functions are called primal lower nice furthermore we use our extensions to derive a relationship between the second order epi derivatives of primal lower nice functions and the proto derivative of their associated subgradient mappings

an effective near field far field transformation technique from truncated and inaccurate amplitude only data a general approach to the near field far field transformation from amplitude only near field data is presented the estimation of the far field is stated as an intersection finding problem and is solved by the minimization of a suitable functional the difficulties related to the possible trapping of the algorithm by a false solution common to any nonlinear inverse problem are mitigated by setting the problem in the space of the squared field amplitudes as already done in a number of existing papers and by incorporating all the a priori knowledge concerning the system under test in the formulation of the problem accordingly the a priori information concerning the far field the near field outside the measurement region and the accuracy of the measurement setup and its dynamic range are properly taken into account in the objective functional the intrinsic ill conditioning of the problem is managed by adopting a general flexible and nonredundant sampling representation of the field which takes into account the geometrical characteristics of the source as a consequence the number of unknowns is minimized and a technique is obtained which easily matches the available knowledge concerning the behavior of the field the effectiveness of the approach is shown by reporting the main results of an extensive numerical analysis as well as an experimental validation performed by using a very low cost near field facility available at the electronic engineering department university of napoli italy

on the discrepancy principle for iterative and parametric methods to solve linear ill posed equations for the numerical solution of non necessarily well posed linear equations in banach spaces we consider a class of iterative methods which contains well known methods like the richardson iteration if the associated resolvent operator fulfils a condition with respect to a sector it is the purpose of this paper to show that for given noisy right hand side the discrepancy principle being a stopping rule for the iteration methods belonging to the mentioned class defines a regularization method and convergence rates are proved under additional smoothness conditions on the initial error this extends similar results obtained for positive semidefinite problems in hilbert spaces then we consider a class of parametric methods which under the same resolvent condition contains the method of the abstract cauchy problem and under a weaker resolvent condition the iterated method of lavrentiev a modified discrepancy principle is formulated for them and finally numerical illustrations are presented

differentiability properties of the minimum time function for normal linear systems abstract a result by sussmann 32 implying that the minimum time function t for normal linear systems is analytic out of a locally finite union of analytic submanifolds is revisited the original proof relies on classical properties of subanalytic sets a constructive and simpler proof is given of a part of it we show that the singular i e the nondifferentiability set of t is contained in a lower dimensionally rectifiable set which can be identified through suitable properties of the switching function our approach extends to large times the strategy initiated by hajek in 23 furthermore a result on the propagation of singularities of non lipschitz type is proved finally we give explicit formulas for the propagation of first and second order partial derivatives of t along optimal trajectories and we prove that normal cones to the epigraph of t at each x t x and to the sublevel of t at x have the same dimension

error analysis of krylov methods in a nutshell error and residual bounds for the matrix iteration methods bicg qmr fom and gmres are derived in a simple and unified way

decomposition methods for large linear discrete ill posed problems the solution of large linear discrete ill posed problems by iterative methods continues to receive considerable attention this paper presents decomposition methods that split the solution space into a krylov subspace that is determined by the iterative method and an auxiliary subspace that can be chosen to help represent pertinent features of the solution decomposition is well suited for use with the gmres rrgmres and lsqr iterative schemes

strong and weak convexity of sets and functions in this paper we study two classes of sets strongly and weakly convex sets for each class we derive a series of properties which involve either the concept of supporting ball an obvious extension of the concept of supporting hyperplane or the normal cone to the set we also study a class of functions denoted convex which satisfy for arbitrary points x1 and x2 and any value 0 1 the classical inequality of convex functions up to a term 1 x1 x2 2 depending on the sign of the constant the function is said to be strongly or weakly convex we provide characteristic properties of this class of sets and we relate it to strongly and weakly convex sets via the epigraph and the level sets finally we give three applications a separation theorem a sufficient condition for global optimum of a nonconvex programming problem and a sufficient geometrical condition for a set to be a manifold