parameter identification of nonlinear aeroelastic system with time delayed feedback control in this paper an enhanced response sensitivity approach is proposed for parameter identification of nonlinear time delay aeroelastic systems two common aeroelastic models are investigated namely

a quasi reversibility regularization method for an inverse heat conduction problem without initial data in this paper we study an inverse heat conduction problem without initial data in a bounded domain in which the cauchy data at x 0 are given and the solution in 0

a fast multiple scale polynomial solution for the inverse cauchy problem of elasticity in an arbitrary plane domain the polynomial expansion method together with the collocation technique is a cheap yet simple method to solve the navier equations of elasticity which is easily arranged to satisfy the governing equations and boundary conditions pointwise in this paper we propose a novel numerical algorithm for the solution of an overspecified underspecified cauchy problem of linear elasticity in an arbitrary plane domain by using the multiple scale pascal polynomial expansion method mspem of which the scales are determined a priori by the collocation points according to the idea of equilibrated matrix in the numerical tests of a direct problem as well as the overspecified underspecified cauchy problems the mspem is very accurate and stable against large relative noise up to 20 for the unknown displacements recovery problem and up to 100 absolute noise for the recovery of unknown loading force the present method is convergent very fast for most cases within 100 iteration steps

direct numerical identification of boundary values in the laplace equation an inverse boundary value problem for the laplace equation is considered the dirichlet and the neumann data are prescribed on respective part of the boundary while there is the second part of the boundary where no boundary data are given there is the third part of the boundary where the robin condition is prescribed this ill posed problem of finding unknown values along the whole boundary is reformulated in terms of the variational problem which is then recast into primary and adjoint boundary value problems of the laplace equation in conventional forms a direct method for numerical solution of the boundary value problems using the boundary element method is presented

the backus gilbert method and their minimum norm solution abstractthis paper has two objectives one is to review the backus gilbert bg method backus and gilbert investigate continuous inverse problems in a radially symmetric earth using an approach completely different from that of standard inversion methods if m is an earth property of interest the bg method provides average values of m over some radial intervals if an interval w is relatively short and centered near a particular radius r0 the bg average will be a local average of m near r0 with a resolving length of w backus and gilbert also introduce the concept of trade off between resolution and error which is essential in inverse theory regardless of the inversion method in spite of its importance inverse theory texts neither describe the bg method in full nor show how to apply it in all its generality because the three papers that introduce the bg method are mathematically difficult this paper provides background material and a detailed derivation of the method as well as two completely wor

contrast source inversion methods in elastodynamics in this paper a nonlinear inversion method is presented for determining the mass density of an elastic inclusion from the knowledge of how the inclusion scatters known incident elastic waves the algorithm employed is an extension of the multiplicative regularized contrast source inversion method mr csi to elasticity this method involves alternate determination of the mass density contrast and the contrast sources the product of the contrast and the fields in each iterative step the simple updating schemes of the method allow the introduction of an extra regularization term to the cost functional as a multiplicative constraint this so called mr csi method mr csi has been proven to be very effective for the acoustic and electromagnetic inverse scattering problems numerical examples demonstrate that the mr csi method shows excellent edge preserving properties by robustly handling noisy data very well even for more complicated elastodynamic problems

sirt and cg type methods for the iterative solution of sparse linear least squares problems abstract sirt and cg type methods have been successfully employed for the approximate solution of least squares problems arising in tomography in this paper we study and compare their convergence and regularization properties it is pointed out that sirt methods apply an uncontrollable implicit rescaling which affects the statistical characteristics of the system whereas cg type methods do not for a large class of model problems it is shown that virtually the same solutions as obtained by sirt methods can be obtained by applying a cg type method to a properly rescaled system but with an amount of work proportional to the square root of the amount of work with sirt

on computing first and second order derivative spectra enhancing resolution in spectral response and an ability to differentiate spectral mixing in delineating the endmembers from the spectral response are central to the spectral data analysis first and higher order derivatives analysis of absorbance and reflectance spectral data is commonly used techniques in differentiating the spectral mixing but high sensitivity of derivative to the noise in data is a major problem in the robust estimation of derivative of spectral data an algorithm of robust estimation of first and second order derivative spectra from evenly spaced noisy normal spectral data is proposed the algorithm is formalized in the framework of an inverse problem where based on the fundamental theorem of calculus a matrix equation is formed using a volterra type integral equation of first kind a regularization technique where the balancing principle is used in selecting a posteriori optimal regularization parameter is designed to solve the inverse problem for robust estimation of first order derivative spectra the higher order derivative spectra are obtained while using the algorithm in sequel the algorithm is tested successfully with synthetically generated spectral data contaminated with additive white gaussian noise and also with real absorbance and reflectance spectral data for fresh and sea water respectively robust and efficient algorithm of computing first and second orders derivative spectra is designed the algorithm is based on the premise of inverse problem where a robust solution is achieved via regularization it couples discrepancy and balancing principles to determine regularization parameter and implement stopping rule respectively numerical experiments on noisy data suggest superiority of the method over finite difference and fourier transform based techniques the proposed method is applied on absorbance and reflectance spectral data for fresh and sea water

inverse scattering for impedance schrodinger operators i step like impedance lattice abstract we study the scattering problem for schrodinger operators in impedance form with step like impedance functions in this paper the case where the jumps are located at the vertices of periodic lattice is considered the set of reflection coefficients is completely described and the scattering map is shown to be homeomorphic also an algorithm reconstructing the impedance function from the reflection coefficient is developed

the 2 norm of random matrices abstract numerical experiments show that it is possible to derive simple estimates for the expected 2 norm of random matrices a with elements from a normal distribution with zero mean and standard deviation and from a poisson distribution with mean value these estimates are max m n 2 max m n and e 2 mn respectively where m and n are the dimensions of a

the optimal projection equations with petersen hollot bounds robust stability and performance via fixed order dynamic compensation for systems with structured real valued parameter uncertainty a feedback control design problem involving structured real valued plant parameter uncertainties is considered a quadratic lyapunov bound suggested by recent work of i r petersen and c v hollot 1986 is utilized in conjunction with the guaranteed cost approach of s s l chang and t k c peng 1972 to guarantee robust stability with robust performance bound necessary conditions that generalize the optimal projection equations for fixed order dynamic compensation are used to characterize the controller that minimizes the performance bound the design equations thus effectively serve as sufficient conditions for synthesizing dynamic output feedback controllers that provide robust stability and performance

adaptive choice of the tikhonov regularization parameter to solve ill posed linear algebraic equations via liapunov optimizing control numerical problems including linear algebraic equations are frequently ill posed which means that small perturbations in the observation data can have large effects on the computed solutions in these cases some kind of regularization method must be used to find a feasible solution regularization implies the modification of the original ill posed problem so that it becomes well posed and the tikhonov regularization method is the most often used this method requires the choice of a regularization parameter and this choice is a crucial issue recently several papers were presented proposing adaptive tikhonov regularization parameters instead of constant ones this paper revisits all these adaptive choices and shows that they can be interpreted in a unified and systematic manner using the liapunov optimizing control loc method which in addition opens up the possibility of new choices of the regularization parameter examples of matrices from real applications show that one of the methods designed by the loc method called the ovm method by its discoverer can even outperform the cg method for some matrices although the cg method performs better for a larger class of matrices

the optimal projection equations for model reduction and the relationships among the methods of wilson skelton and moore first order necessary conditions for quadratically optimal reduced order modeling of linear time invariant systems are derived in the form of a pair of modified lyapunov equations coupled by an oblique projection which determines the optimal reduced order model this form of the necessary conditions considerably simplifies previous results of wilson 1 and clearly demonstrates the quadratic extremality and nonoptimality of the balancing method of moore 2 the possible existence of multiple solutions of the optimal projection equations is demonstrated and a relaxation type algorithm is proposed for computing these local extrema a component cost analysis of the model error criterion similar to the approach of skelton 3 is utilized at each iteration to direct the algorithm to the global minimum

an analysis of the zero crossing method for choosing regularization parameters solving discrete ill posed problems via tikhonov regularization introduces the problem of determining a regularization parameter there are several methods available for choosing such a parameter yet in general the uniqueness of this choice is an open question two empirical methods for determining a regularization parameter which appear in the biomedical engineering literature are the composite residual and smoothing operator and the zero crossing method an equivalence is established between the zero crossing method and a minimum product criterion which has previously been linked with the l curve method finally the uniqueness of a choice of regularization parameter is established under certain restrictions on the fourier coefficients of the data in the ill posed problem

meshless thin plate spline methods for the modified helmholtz equation in this paper we investigate the application of the meshless radial basis function method for solving the helmholtz equation using thin plate splines we use a meshless method mixed with a boundary and a fundamental solution methods the numerical computation is achieved by using the generalized minimal residual gmres the least square lsqr methods associated with tikhonov regularization

robust reduced order nonstrictly proper state estimation via the optimal projection equations with petersen hollot bounds a state estimation design problem involving parametric plant uncertainties is considered an error bound suggested by recent work of petersen and hollot is utilized for guaranteeing robust estimation necessary conditions which generalize the optimal projection equations for reduced order state estimation are used to characterize the estimator which minimizes the error bound the design equations thus effectively serve as sufficient conditions for synthesizing robust estimators an additional feature is the presence of a static estimation gain in conjunction with the dynamic kalman estimator i e a nonstrictly proper estimator

a multiple direction trefftz method for solving the multi dimensional wave equation in an arbitrary spatial domain in this paper we first express the wave equation in terms of the minkowskian polar coordinates and generate a set of complete hyperbolic type trefftz bases r k cosh k and r k sinh k which are further transformed to wave polynomials as the trial solution bases for the one dimensional wave equation in order to stably solve the wave propagation problems long term we develop a multiple scale trefftz method mstm of which the scales are determined a priori by the collocation points then we derive a very simple method of multi dimensional wave polynomials equipped with different spatial directions which being the normalized wavenumber vectors as the polynomial trefftz bases for solving the multi dimensional wave equations which is named a multiple direction trefftz method mdtm several numerical examples of two and three dimensional wave equations demonstrate that the present method is efficient and stable

inverse scattering for discontinuous impedance schrodinger operators a model example we discuss the possibility of applying the classical reconstruction procedure in the inverse scattering problems for schr odinger operators in impedance form with a non smooth impedance we illustrate on a simple model example that the formal application of the classical algorithm gives a wrong result whereas an approach based on regularization leads in the limit to a correct reconstruction of the impedance function

a globally optimal tri vector method to solve an ill posed linear system in the present paper a future cone in the minkowski space defined in terms of the square norm of the residual vector for an ill posed linear system to be solved is used to derive a nonlinear system of ordinary differential equations then the forward euler scheme is used to generate an iterative algorithm two critical values in the critical descent tri vector are derived which lead to the largest convergence rate of the resultant iterative algorithm namely the globally optimal tri vector method gotvm some numerical examples are used to reveal the superior performance of the gotvm than the famous methods of conjugate gradient cgm and generalized minimal residual gmres through the numerical tests we also set forth the rationale by assuming the tri vector as being a better descent direction

a first order lyapunov robustness method for linear systems with uncertain parameters a method for stability robustness analysis based on a quadratic lyapunov function that varies linearly with uncertainty parameters is derived linear time invariant systems with structured uncertainties are discussed the lyapunov function is optimized numerically to maximize the robustness region in parameter space numerical results are given for four examples in which the first order method is compared to previous lyapunov methods for robustness analysis while the zero order method is slightly better than the first order method for one example the first order method is clearly superior in the other three more realistic examples the first order method is especially superior for applications to active control of flexible structures where robustness with respect to unmodeled coupling between modeled modes are important issues for such applications the first order method is much better at detecting the increased robustness associated with increased separation between frequencies

full waveform static corrections using blind channel identification near surface wavefield perturbations can be very complex and completely mask the target reflections despite this complexity conventional methods rely on parameterizations characterized by simple time and amplitude anomalies to compensate for these perturbations determining and compensating for time shifts is generally referred to as residual static corrections whereas surface consistent deconvolution techniques deal with amplitude anomalies we present an approach that uses the full waveform to parameterize near surface perturbations therefore we refer to this method as waveform statics important differences from conventional static corrections are that this approachallowstimeshiftstovarywithfrequencyandtakesamplitudevariationsdirectlyintoaccount furthermore theprocedure is fully automated and does not rely on near surface velocity information the waveform static corrections are obtained using blind channel identification and applied to the recordings using multichannel deconvolution as a result the method implicitly incorporates array forming the developed method is validated onsyntheticdataandappliedtopartofafielddatasetacquiredin an area with significant near surface heterogeneity the source and receiver responses obtained are strongly correlated to the near surfaceconditionsandshowchanges bothinphaseandfrequency content along the spread the application of the waveform statics demonstrates that they not only correct for near surface wavefield perturbations but also strongly reduce coherent noise this results in substantial improvements both in trace totrace coherency and in depth resolution in addition the procedure delineates reflection events that are difficult to detect prior to our proposed correction based on these results we conclude that complex near surface perturbations can be successfully dealt with using the multichannel full waveform static correctionprocedure

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

recovering the density of a string from only lowest frequency data a classical inverse problem is can you hear the density of a string clamped at both ends the answer as narrowly stated is negative one has to give an additional data sequence such as the energy in each mode norming constants or information on the string slope at the endpoints or alternatively change the boundary conditions and obtain the new frequencies what if neither of these options is possible one solution recently proposed was to add a known mass density and remeasure the dirichlet spectrum w rundell and p e sacks siam j appl math 73 2013 pp 1020 1037 in this work we take a related approach we are able to add any number of known mass densities but we can only measure the fundamental frequency that is the lowest eigenvalue in each case we will show that our problem can be closely approximated by a related problem for which there is uniqueness and we discuss a suite of reconstruction methods

the optimal projection equations for reduced order state estimation first order necessary conditions for optimal steady state reduced order state estimation for a linear time invariant plant in the presence of correlated disturbance and nonsingular measurement noise are derived in a new and highly simplified form in contrast to the lone matrix riccati equation arising in the full order kalman filter case the optimal steady state reduced order estimator is characterized by three matrix equations one modified riccati equation and two modified lyapunov equations coupled by a projection whose rank is precisely equal to the order of the estimator and which determines the optimal estimator gains this coupling is a graphic reminder of the suboptimality of proposed approaches involving either model reduction followed by full order estimator design or full order estimator design followed by estimator reduction techniques the results given here complement recently obtained results which characterize the optimal reduced order model by means of a pair of coupled modified lyapunov equations 7 and the optimal fixed order dynamic compensator by means of a coupled system of two modified riceati equations and two modified lyapunov equations 6

model reduction via balanced realizations an extension and frequency weighting techniques two model reduction methods for discrete systems related to balanced realizations are described the first is a technique which utilizes the least controllable and observable subsystem in deriving a balanced discrete reduced order model for this technique as l sup infinity norm bound on the reduction error is given the second method is a frequency weighting technique for discrete and continuous time systems where the input normal or output normal realizations are modified to include a simple frequency weighting for this technique l sup infinity norm bounds on the weighted reduction errors are obtained

asymptotic theory of filtering for linear operator equations with discrete noisy data on considere les equations integrales de fredholm de premiere espece a noyaux continus avec echantillonnage des donnees et alteration par le bruit blanc on etablit une condition suffisante de convergence des methodes de filtrage

a lyapunov robustness bound for linear systems with periodic uncertainties abstract for linear systems involving uncertain parameters with known constant nominal values and uncertain perturbations that vary sinusoidally with time lyapunov robustness anslysis is used to determine a stability bound or margin for the amplitudes of the parameter perturbations this bound is the size of a hypercube in parameter space for which asymptotic stability is guaranteed the bound which is based on a quadratic lyapunov function that depends linearly on parameter perturbations varies with the frequency of the uncertain parameter perturbations the bound is asymptotically proportional to the square root of this frequency as it becomes large

planar crack identification in 3d linear elasticity by the reciprocity gap method abstract we study the reciprocity gap method andrieux et al 1999 for the identification of planar cracks in the framework of three dimensional linear elasticity in order to achieve better accuracy on thick domains we propose to use polynomial test functions instead of fourier series we also propose to improve the solution by various regularization techniques that are tested and compared numerical assessments are provided in 2d and 3d

a state space force identification method based on markov parameters precise computation and regularization technique a time domain force identification approach for linear system is proposed this approach can found a highly precise force identification model within the scope of general computer precision while it does not cost much computing time although the force identification model is accurate the force identification process like other inverse methods is still ill posed due to the inversion process and the white noise in measured structural responses the singular value decomposition is used to reveal the intrinsically matter of the ill posedness of force identification problem and a regularization technique is utilized to deal with this issue finally the proposed method with the aid of regularization technique is successfully applied to identify the input forces in two numerical simulations

optimally scaled vector regularization method to solve ill posed linear problems instead of the tikhonov regularization method which with a scalar being the regularization parameter liu et al 1 have proposed a novel regularization method with a vector as being the regularization parameter as a continuation we further propose an optimally scaled vector regularization method osvrm to solve the ill posed linear problems which is better than the tikhonov regularization method the presently proposed vector regularization method is shown to be well conditioning to overcome the ill posedness of the linear equations system the osvrm causes a significant improvement of stability and accuracy in the numerical solution of ill posed linear problem and its convergence speed is as fast as by solving the well posed linear problem some tests of the linear inverse problems confirm the efficiency and accuracy of the osvrm

boundary identification for a 3d laplace equation using a genetic algorithm in this paper we consider the identification of the geometric structure of the boundary of the solution domain for the three dimensional laplace equation we investigate the determination of the shape of an unknown portion of the boundary of a solution domain from cauchy data on the remaining portion of the boundary this problem arises in the study of quantitative non destructive evaluation of corrosion in materials in which boundary measurements of currents and voltages are used to determine the material loss caused by corrosion the domain identification problem is considered as a variational problem to minimize a defect functional which utilises some additional data on certain known parts of the boundary a real coded genetic algorithm rcga is used in order to minimise the objective functional the unknown boundary is parameterized using b splines the laplace equation is discretised using the method of fundamental solutions mfs numerical results are presented and discussed for several test examples

improved estimation of subject level functional connectivity using full and partial correlation with empirical bayes shrinkage abstract reliability of subject level resting state functional connectivity fc is determined in part by the statistical techniques employed in its estimation methods that pool information across subjects to inform estimation of subject level effects e g bayesian approaches have been shown to enhance reliability of subject level fc however fully bayesian approaches are computationally demanding while empirical bayesian approaches typically rely on using repeated measures to estimate the variance components in the model here we avoid the need for repeated measures by proposing a novel measurement error model for fc describing the different sources of variance and error which we use to perform empirical bayes shrinkage of subject level fc towards the group average in addition since the traditional intra class correlation coefficient icc is inappropriate for biased estimates we propose a new reliability measure denoted the mean squared error intra class correlation coefficient iccmse to properly assess the reliability of the resulting biased estimates we apply the proposed techniques to test retest resting state fmri data on 461 subjects from the human connectome project to estimate connectivity between 100 regions identified through independent components analysis ica we consider both correlation and partial correlation as the measure of fc and assess the benefit of shrinkage for each measure as well as the effects of scan duration we find that shrinkage estimates of subject level fc exhibit substantially greater reliability than traditional estimates across various scan durations even for the most reliable connections and regardless of connectivity measure additionally we find partial correlation reliability to be highly sensitive to the choice of penalty term and to be generally worse than that of full correlations except for certain connections and a narrow range of penalty values this suggests that the penalty needs to be chosen carefully when using partial correlations

the optimal projection equations for fixed order dynamic compensation first order necessary conditions for quadratically optimal steady state fixed order dynamic compensation of a linear time invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form in contrast to the pair of matrix riccati equations for the full order lqg case the optimal steady state fixed order dynamic compensator is characterized by four matrix equations two modified riccati equations and two modified lyapunov equations coupled by a projection whose rank is precisely equal to the order of the compensator and which determines the optimal compensator gains the coupling represents a graphic portrayal of the demise of the classical separation principle for the reduced order controller case

relations between svd and gsvd of discrete regularization problems in standard and general form abstract we consider an algorithm due to elden that transforms general discrete regularization problems into standard form we derive a simple relationship between the svd associated with the standard form problem and the gsvd associated with the general problem and we discuss the accuracy of the gsvd computed via this transformation

blind separation of sound sources from the principle of least spatial entropy abstract the aim of the paper is to offer a method for separating incoherent and compact sound sources which may overlap in both the space and frequency domains this is found of interest in acoustical applications involving the identification and ranking of sound sources stemming from different physical origins the principle proceeds in two steps the first one being reminiscent to source reconstruction e g as in near field acoustical holography and the second one to blind source separation specifically the source mixture is first expanded into a linear combination of spatial basis functions whose coefficients are set by backpropagating the pressures measured by an array of microphones to the source domain this leads to a formulation similar but no identical to blind source separation in the second step these coefficients are blindly separated into uncorrelated latent variables assigned to incoherent virtual sources these are shown to be defined up to an arbitrary rotation a unique set of sound sources is finally recovered by searching for that rotation by conjugate gradient descent in the stiefel manifold of unitary matrices which maximizes their spatial compactness as measured either by their spatial variance or their spatial entropy this results in the proposal of two separation criteria coined least spatial variance and least spatial entropy respectively the same concept of spatial entropy which is central to the paper is also exploited in defining a new criterion the entropic l curve dedicated to determining the number of active sound sources the idea consists in considering the number of sources that achieves the best compromise between a low spatial entropy as expected from compact sources and a low statistical entropy as expected from a low residual error the proposed methodology is validated on both laboratory experiments and numerical data and illustrated on an industrial example concerned with the ranking of sound sources on a diesel engine at the same time its robustness to the estimated number of active sources is demonstrated

a riccati equation approach to the stabilization of uncertain linear systems this paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems the systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set furthermore these uncertain parameters may be time varying the method used to establish asymptotic stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic lyapunov function once the lyapunov function has been obtained it is used to construct the stabilizing feedback control law the fundamental idea behind the algorithm presented involves constructing an upper bound for the lyapunov derivative corresponding to the closed loop system this upper bound is a quadratic form by using this upper bounding procedure a suitable lyapunov function can be found by solving a certain matrix riccati equation another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic lyapunov function

a regularized inverse approach to ultrasonic pulse echo imaging an inverse theoretic approach to ultrasonic pulse echo imaging based on nonquadratic regularization is presented and its effectiveness is investigated computationally by 1 evaluating the quality of the reconstruction of speckle based images as a function of the transmit receive bandwidth and focal number of the transducer 2 comparing the reconstructed images with those obtained by using conventional b mode imaging the l curve and the generalized cross validation methods were evaluated as automatic regularization parameter selection techniques the inversion using regularization produced better results than conventional b mode imaging for high signal to noise ratios snrs a lower bound of 30 db for the snr was found for this study below which several of the image features were lost during the reconstruction process in order to control the distortion due to the noise

a new method for nmr data inversion based on double parameter regularization nuclear magnetic resonance nmr technology plays a significant role in petroleum exploration nmr data can be processed using inversion methods to reflect the relaxation information of all the components a new double parameter regularization dpr method was proposed for the inversion of nmr data whose regularization terms consist of tikhonov regularization and maximum entropy regularization the objective function for the dpr method was solved using the levenberg marquardt method the proportional coefficient of the regularization parameter was obtained using an iteration procedure the optimum regularization parameter of the dpr method was selected using an s curve the relationship between the optimum regularization parameter and the signal to noise ratio snr of the data was evaluated moreover we compared the results of the nmr inversion obtained from the norm smooth method the maximum entropy method and the dpr method for simulated data we evaluated how the proportional coefficient of the re

structural damping identification based on an iterative regularization method a time domain structural damping identification method is presented in this paper the damping of a structure is assumed to be time invariant rayleigh damping time variant rayleigh damping and modal damping respectively and an iterative regularization method is proposed to identify these three types of damping in turn a sensitivity approach is adopted in the formulation of the ill posed inverse problem a new constraint is imposed on the identified iterative increment as well as on the unknown structural parameters to ensure their physical meaning in the identification process is not lost the proposed method is verified in numerical studies with a space frame structure and laboratory measurements of accelerations with accurate results

regularization parameter selection for nonlinear iterative image restoration and mri reconstruction using gcv and sure based methods regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values we focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive possibly complex gaussian noise generalized cross validation gcv and weighted mean squared error mse approaches based on stein s unbiased risk estimate sure need the jacobian matrix of the nonlinear reconstruction operator representative of the iterative algorithm with respect to the data we derive the desired jacobian matrix for two types of nonlinear iterative algorithms a fast variant of the standard iterative reweighted least squares method and the contemporary split bregman algorithm both of which can accommodate a wide variety of analysis and synthesis type regularizers the proposed approach iteratively computes two weighted sure type measures predicted sure and projected sure which require knowledge of noise variance 2 and gcv which does not need 2 for these algorithms we apply the methods to image restoration and to magnetic resonance image mri reconstruction using total variation and an analysis type l1 regularization we demonstrate through simulations and experiments with real data that minimizing predicted sure and projected sure consistently lead to near mse optimal reconstructions we also observe that minimizing gcv yields reconstruction results that are near mse optimal for image restoration and slightly suboptimal for mri theoretical derivations in this paper related to jacobian matrix evaluations can be extended in principle to other types of regularizers and reconstruction algorithms

scattering for general type dirac systems on the semi axis reflection coefficients and weyl functions abstract we show that for general type self adjoint and skew self adjoint dirac systems on the semi axis weyl functions are unique analytic extensions of the reflection coefficients new results on the extension of the weyl functions to the real axis and on the existence in the skew self adjoint case of the weyl functions follow important procedures to recover general type dirac systems from the weyl functions are applied to the recovery of dirac systems from the reflection coefficients we explicitly recover dirac systems from the rational reflection coefficients as well

the polynomial trefftz method for solving backward and inverse source wave problems the trefftz method is a truly meshless boundary type method because the trial solutions automatically satisfy the governing equation in order to stably solve the high dimensional backward wave problems and the one dimensional inverse source problems we develop a multiple scale polynomial trefftz method msptm of which the scales are determined a priori by the collocation points the msptm can retrieve the missing initial data and unknown time varying wave source the present method can also be extended to solve the higher dimensional wave equations long term through the introduction of a director in the two dimensional polynomial trefftz bases several numerical examples reveal that the msptm is efficient and stable for solving severely ill posed inverse problems of wave equations under large noises

a multiple scale pascal polynomial for 2d stokes and inverse cauchy stokes problems abstract the polynomial expansion method is a useful tool for solving both the direct and inverse stokes problems which together with the pointwise collocation technique is easy to derive the algebraic equations for satisfying the stokes differential equations and the specified boundary conditions in this paper we propose two novel numerical algorithms based on a third first order system and a third third order system to solve the direct and the inverse cauchy problems in stokes flows by developing a multiple scale pascal polynomial method of which the scales are determined a priori by the collocation points to assess the performance through numerical experiments we find that the multiple scale pascal polynomial expansion method mspem is accurate and stable against large noise

robust reduced order modeling via the optimal projection equations with peterson hollot bounds an optimal reduced order modeling problem with parametric plant uncertainty is considered a model reduction bound suggested by recent work of i r petersen and c v hollot is utilized for guaranteeing robust reduced order modeling over a specified range of uncertain parameters necessary conditions which generalize the optimal projection equations for model reduction are used to characterize the reduced order model which minimizes the model reduction bound the optimality equations thus effectively serve as sufficient conditions for characterizing robust reduced order models