the superlinear convergence of a new quasi newton sqp method for constrained optimization in this paper a new variation of the quasi newton sqp methods for constrained optimization is proposed under some suitable assumptions the superlinear convergence of the new method has been established

a constrained min max algorithm for rival models of the same economic system there are well established rival theories about the economy these have in turn led to the development of rival models purporting to represent the economic system the models are large systems of discrete time nonlinear dynamic equations observed data of the real system does not in general provide sufficient information for statistical methods to invalidate all but one of the rival models in such a circumstance there is uncertainty about which model to use in the formulation of policy prudent policy design would suggest that a model based policy should take into account all the rival models this is achieved as a pooling of the models the pooling that yields the policy which is robust to model choice is formulated as a constrained min max problem the minimization is over the decision variables and the maximization is over the rival models only equality constraints are considered

the scale representation the authors considers scale a physical attribute of a signal and develop its properties he presents an operator which represents scale and study its characteristics and representation this allows one to define the scale transform and the energy scale density spectrum which is an indication of the intensity of scale values in a signal he obtains explicit expressions for the mean scale scale bandwidth instantaneous scale and scale group delay furthermore he derives expressions for mean time mean frequency duration frequency bandwidth in terms of the scale variable the short time transform is defined and used to obtain the conditional value of scale for a given time he shows that as the windows narrows one obtains instantaneous scale convolution and correlation theorems for scale are derived a formulation is devised for studying linear scale invariant systems he derives joint representations of time scale and frequency scale general classes for each are presented using the same methodology as for the time frequency case as special cases the joint distributions of marinovich altes 1978 1986 and bertrand bertrand 1984 are recovered also joint representations of the three quantities time frequency scale are devised a general expression for the local scale autocorrelation function is given uncertainty principles for scale and time and scale and frequency are derived

design of time frequency representations using a multiform tiltable exponential kernel a novel cohen s 1981 class time frequency representation with a tiltable generalized exponential kernel capable of attaining a wide diversity of shapes in the ambiguity function plane is proposed for improving the time frequency analysis of multicomponent signals the first advantage of the proposed kernel is its ability to generate a wider variety of passband shapes e g rotated ellipses generalized hyperbolas diamonds rectangles parallel strips at arbitrary angles crosses snowflakes etc and narrower transition regions than conventional cohen s class kernels this versatility enables the new kernel to suppress undesirable cross terms in a broader variety of time frequency scenarios the second advantage of the new kernel is that closed form design equations can now be easily derived to select kernel parameters that meet or exceed a given set of user specified passband and stopband design criteria in the ambiguity function plane thirdly it is shown that simple constraints on the parameters of the new kernel can be used to guarantee many desirable properties of time frequency representations the well known choi williams 1989 exponential kernel the generalized exponential kernel and nuttall s 1990 tilted gaussian kernel are special cases of the proposed kernel

the fractional fourier transform and time frequency representations the functional fourier transform frft which is a generalization of the classical fourier transform was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community to which it may however be potentially useful the frft depends on a parameter spl alpha and can be interpreted as a rotation by an angle spl alpha in the time frequency plane an frft with spl alpha spl pi 2 corresponds to the classical fourier transform and an frft with spl alpha 0 corresponds to the identity operator on the other hand the angles of successively performed frfts simply add up as do the angles of successive rotations the frft of a signal can also be interpreted as a decomposition of the signal in terms of chirps the authors briefly introduce the frft and a number of its properties and then present some new results the interpretation as a rotation in the time frequency plane and the frft s relationships with time frequency representations such as the wigner distribution the ambiguity function the short time fourier transform and the spectrogram these relationships have a very simple and natural form and support the frft s interpretation as a rotation operator examples of frfts of some simple signals are given an example of the application of the frft is also given

a class of high order runge kutta chebyshev stability polynomials the analytic form of a new class of factorized runge kutta chebyshev frkc stability polynomials of arbitrary order n is presented roots of frkc stability polynomials of degree l m n are used to construct explicit schemes comprising l forward euler stages with internal stability ensured through a sequencing algorithm which limits the internal amplification factors to l 2 the associated stability domain scales as m 2 along the real axis marginally stable real valued points on the interior of the stability domain are removed via a prescribed damping procedure by construction frkc schemes meet all linear order conditions for nonlinear problems at orders above 2 complex splitting or butcher series composition methods are required linear order conditions of the frkc stability polynomials are verified at orders 2 4 and 6 in numerical experiments comparative studies with existing methods show the second order unsplit frkc2 scheme and higher order 4 and 6 split frkcs schemes are efficient for large moderately stiff problems

pirock a swiss knife partitioned implicit explicit orthogonal runge kutta chebyshev integrator for stiff diffusion advection reaction problems with or without noise a partitioned implicit explicit orthogonal runge kutta method pirock is proposed for the time integration of diffusion advection reaction problems with possibly severely stiff reaction terms and stiff stochastic terms the diffusion terms are solved by the explicit second order orthogonal chebyshev method rock2 while the stiff reaction terms solved implicitly and the advection and noise terms solved explicitly are integrated in the algorithm as finishing procedures it is shown that the various coupling between diffusion reaction advection and noise can be stabilized in the pirock method the method implemented in a single black box code that is fully adaptive provides error estimators for the various terms present in the problem and requires from the user solely the right hand side of the differential equation numerical experiments and comparisons with existing chebyshev methods imex methods and partitioned methods show the efficiency and flexibility of our new algorithm

constrained pose refinement of parametric objects pose refinement is an essential task for computer vision systems that require the calibration and verification of model and camera parameters typical domains include the real time tracking of objects and verification in model based recognition systems a technique is presented for recovering model and camera parameters of 3d objects from a single two dimensional image this basic problem is further complicated by the incorporation of simple bounds on the model and camera parameters and linear constraints restricting some subset of object parameters to a specific relationship it is demonstrated in this paper that this constrained pose refinement formulation is no more difficult than the original problem based on numerical analysis techniques including active set methods and lagrange multiplier analysis a number of bounded and linearly constrained parametric models are tested and convergence to proper values occurs from a wide range of initial error utilizing minimal matching information relative to the number of parameters and components the ability to recover model parameters in a constrained search space will thus simplify associated object recognition problems

a time frequency formulation of optimum detection a time frequency formulation is proposed for the optimum detection of gaussian signals in white gaussian noise by choosing the wigner ville distribution as the basic time frequency tool it is shown that the corresponding receivers generally take the form of a correlation between time frequency structures matching mathematical optimality with a physically meaningful interpretation the case of low snr is examined and various examples are considered deterministic signal rayleigh fading signal random jitter and random time varying channel a general class of time frequency receivers is proposed which admits as limiting cases different known structures and its suboptimum performance is evaluated possible extensions to more elaborate situations including parameter estimation are mentioned

on generalized marginal time frequency distributions we introduce a family of time frequency tf distributions with generalized marginals i e beyond the time domain and the frequency domain marginals in the sense that the projections of a tf distribution along one or more angles are equal to the magnitude squared of the fractional fourier transforms of the signal we present a necessary and sufficient condition for a tf distribution in cohen s class to satisfy generalized marginals we then modify the existing well known tf distributions in cohen s class such as choi williams 1989 and page distributions so that the modified ones have generalized marginals numerical examples are presented to show that the proposed tf distributions have the advantages of both wigner ville and other quadratic tf distributions which only have the conventional marginals moreover they also indicate that the generalized marginal tf distributions with proper marginals are more robust than the wigner ville and the choi williams distributions when signals contain additive noise

s rock chebyshev methods for stiff stochastic differential equations we present and analyze a new class of numerical methods for the solution of stiff stochastic differential equations sdes these methods called s rock for stochastic orthogonal runge kutta chebyshev are explicit and of strong order 1 and possess large stability domains in the mean square sense for mean square stable stiff sdes they are much more efficient than the standard explicit methods proposed so far for stochastic problems and give significant speed improvement the explicitness of the s rock methods allows one to handle large systems without linear algebra problems usually encountered with implicit methods numerical results and comparisons with existing methods are reported

serk2v3 solving mildly stiff nonlinear partial differential equations abstract multidimensional nonlinear parabolic partial differential equations pdes appear in a large variety of disciplines usually the scientific literature advises against the use of explicit ode solvers for the integration of stiff problems however in this manuscript we would like to show how some explicit methods can be very efficient for specific problems stabilized explicit runge kutta methods serk are a class of explicit methods with extended stability domains along the negative real axis it is necessary to evaluate the function s times but the stability region is o s 2 hence the computational cost is o s times lower than for traditional explicit algorithms in this way moderately stiff problems can be integrated by the use of simple explicit evaluations serk schemes can easily be applied to many different classes of problems with large dimensions and additionally they have low memory demand since these methods are explicit they do not require algebra routines to solve large nonlinear systems associated to odes and therefore are especially well suited for the method of lines mol discretizations of parabolic multi dimensional pdes additionally the stability domain is adapted precisely to the spectrum of the problem at the current time of integration in an optimal way that is with minimal number of additional stages hence adaptation of the length step is possible at practically no extra cost in this work we study several strategies to change the time step for non smooth functions and finally propose a new technique this procedure improves the numerical results especially when the data is non smooth we also derive two algorithms to estimate the spectral radius in the new code a nonlinear power method and another procedure based on the gershgorin theorem although serk algorithms are only second order schemes in this manuscript we propose to utilize them after higher order discretizations in space to obtain higher accurate solutions efficiently and usually faster since these higher order schemes allow the use of a smaller number of nodes some numerical experiments shown in the paper support these conclusions

second order chebyshev methods based on orthogonal polynomials stabilized methods also called chebyshev methods are explicit runge kutta methods with extended stability domains along the negative real axis these methods are intended for large mildly stiff problems originating mainly from parabolic pdes the aim of this paper is to show that with the use of orthogonal polynomials we can construct nearly optimal stability polynomials of second order with a three term recurrence relation these polynomials can be used to construct a new numerical method which is implemented in a code called rock2 this new numerical method can be seen as a combination of van der houwen sommeijer type methods and lebedev type methods

the integration of stiff initial value problems in odes using modified extended backward differentiation formulae abstract a class of modified extended backward differentiation formulae mebdf suitable for the approximate numerical integration of first order systems of stiff ordinary differential equations is introduced the computational aspects of this new class of formulae are examined in detail in particular algorithms for varying both order and stepsize are given and this leads to a variable step variable order process using highly stable formulae of order 2 8 extensive numerical results for the well known detest set are given and on this basis a comparison is made between a code incorporating mebdf a code due to hindmarsh based on conventional backward differentiation formulae and a code due to skeel and kong based on blended linear multistep methods it is shown that on this test set the mebdf code is very reliable and is competitive with the other two codes on a significant class of problems a computer listing of the mebdf code used to obtain the results presented in this paper is available from the author

on the convergence of a new trust region algorithm in this paper we present a new trust region algorithm for general nonlinear constrained optimization problems the algorithm is based on the l infty exact penalty function under very mild conditions global convergence results for the algorithm are given local convergence properties are also studied it is shown that the penalty parameter generated by the algorithm will be eventually not less than the l 1 norm of the lagrange multipliers at the accumulation point it is proved that the method is equivalent to the sequential quadratic programming method for all large k hence superlinearly convergent results of the sqp method can be applied numerical results are also reported

a recursive quadratic programming algorithm that uses differentiable exact penalty functions in this paper a recursive quadratic programming algorithm for solving equality constrained optimization problems is proposed and studied the line search functions used are approximations to fletcher s differentiable exact penalty function global convergence and local superlinear convergence results are proved and some numerical results are given

exponential integrators for large systems of differential equations we study the numerical integration of large stiff systems of differential equations by methods that use matrix vector products with the exponential or a related function of the jacobian for large problems these can be approximated by krylov subspace methods which typically converge faster than those for the solution of the linear systems arising in standard stiff integrators the exponential methods also offer favorable properties in the integration of differential equations whose jacobian has large imaginary eigenvalues we derive methods up to order 4 which are exact for linear constant coefficient equations the implementation of the methods is discussed numerical experiments with reaction diffusion problems and a time dependent schrodinger equation are included

exponential fitting bdf algorithms explicit and implicit 0 stable methods we present bdf type formulas capable of the exact integration with only round off errors of differential equations the solutions of which belong to the space generated by the linear combinations of 1 eax xeax plots of their 0 stability regions in terms of are provided we will see that the explicit method is 0 stable with many parameters h plots of their regions absolute stability that include all the negative real axis are provided numerical examples show the efficiency of the proposed codes specially when we are integrating stiff problems with the explicit method

construction of positive time frequency distributions a general method for constructing nonnegative definite joint time frequency distributions tfds satisfying the marginals of time s t sup 2 and frequency s f sup 2 is presented as nonnegative definite distributions with the correct marginals these tfds are members of the cohen posch class several examples illustrating properties of these tfds are presented for both synthetic and real signals

essentially optimal explicit runge kutta methods with application to hyperbolic parabolic equations optimal explicit runge kutta methods consider more stages in order to include a particular spectrum in their stability domain and thus reduce time step restrictions this idea so far used mostly for real line spectra is generalized to more general spectra in the form of a thin region in thin regions the eigenvalues may extend away from the real axis into the imaginary plane we give a direct characterization of optimal stability polynomials containing a maximal thin region and calculate these polynomials for various cases semi discretizations of hyperbolic parabolic equations are a relevant application which exhibit a thin region spectrum as a model linear scalar advection diffusion is investigated the second order stabilized explicit runge kutta methods derived from the stability polynomials are applied to advection diffusion and compressible viscous fluid dynamics in numerical experiments due to the stabilization the time step can be controlled solely from the hyperbolic cfl condition even in the presence of viscous fluxes

a global convergence analysis of an algorithm for large scale nonlinear optimization problems in this paper we give a global convergence analysis of a basic version of an sqp algorithm described in p t boggs a j kearsley and j w tolle siam j optim 9 1999 pp 755 778 for the solution of large scale nonlinear inequality constrained optimization problems several procedures and options have been added to the basic algorithm to improve the practical performance some of these are also analyzed the important features of the algorithm include the use of a constrained merit function to assess the progress of the iterates and a sequence of approximate merit functions that are less expensive to evaluate it also employs an interior point quadratic programming solver that can be terminated early to produce a truncated step

smoothing schemes for reaction diffusion systems with nonsmooth data cox and matthews s m cox p c matthews exponential time differencing for stiff systems j comput phys 176 2002 430 455 developed a class of exponential time differencing runge kutta schemes etdrk for nonlinear parabolic equations kassam and trefethen a k kassam ll n trefethen fourth order time stepping for stiff pdes siam j sci comput 26 2005 1214 1233 have shown that these schemes can suffer from numerical instability and they proposed a modified form of the fourth order etdrk4 scheme they use complex contour integration to implement these schemes in a way that avoids inaccuracies when inverting matrix polynomials but this approach creates new difficulties in choosing and evaluating the contour for larger problems neither treatment addresses problems with nonsmooth data where spurious oscillations can swamp the numerical approximations if one does not treat the problem carefully such problems with irregular initial data or mismatched initial and boundary conditions are important in various applications including computational chemistry and financial engineering we introduce a new version of the fourth order cox matthews kassam trefethen etdrk4 scheme designed to eliminate the remaining computational difficulties this new scheme utilizes an exponential time differencing runge kutta etdrk scheme using a diagonal pade approximation of matrix exponential functions while to deal with the problem of nonsmooth data we use several steps of an etdrk scheme using a sub diagonal pade formula the new algorithm improves computational efficiency with respect to evaluation of the high degree polynomial functions of matrices having an advantage of splitting the matrix polynomial inversion problem into a sum of linear problems that can be solved in parallel in this approach it is only required that several backward euler linear problems be solved in serial or parallel numerical experiments are described to support the new scheme

extrapolated stabilized explicit rungekutta methods extrapolated stabilized explicit rungekutta methods eserk are proposed to solve multi dimensional nonlinear partial differential equations pdes in such methods it is necessary to evaluate the function nt times per step but the stability region is o nt2 hence the computational cost is o nt times lower than for a traditional explicit algorithm in that way stiff problems can be integrated by the use of simple explicit evaluations in which case implicit methods usually had to be used therefore they are especially well suited for the method of lines mol discretizations of parabolic nonlinear multi dimensional pdes in this work first s stages first order methods with extended stability along the negative real axis are obtained they have slightly shorter stability regions than other traditional first order stabilized explicit rungekutta algorithms also called rungekuttachebyshev codes later they are used to derive nt stages second and fourth order schemes using richardson extrapolation the stability regions of these fourth order codes include the interval 0 01nt2 0 nt being the number of total functions evaluations which are shorter than stability regions of rock4 methods for example however the new algorithms neither suffer from propagation of errors as other rungekuttachebyshev codes as rock4 or dumka nor internal instabilities additionally many other types of higher order and also lower order methods can be obtained easily in a similar way these methods also allow adaptation of the length step with no extra cost hence the stability domain is adapted precisely to the spectrum of the problem at the current time of integration in an optimal way i e with minimal number of additional stages we compare the new techniques with other well known algorithms with good results in very stiff diffusion or reactiondiffusion multi dimensional nonlinear equations

unitary equivalence a new twist on signal processing unitary similarity transformations furnish a powerful vehicle for generating infinite generic classes of signal analysis and processing tools based on concepts different from time frequency and scale implementation of these new tools involves simply preprocessing the signal by a unitary transformation performing standard processing on the transformed signal and then in some cases transforming the resulting output the resulting unitarily equivalent systems can focus on the critical signal characteristics in large classes of signals and hence prove useful for representing and processing signals that are not well matched by current techniques as specific examples of this procedure we generalize linear time invariant systems orthonormal basis and frame decompositions and joint time frequency and time scale distributions these applications illustrate the utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature

a feasible sequential linear equation method for inequality constrained optimization in this paper by means of the concept of the working set which is an estimate of the active set we propose a feasible sequential linear equation algorithm for solving inequality constrained optimization problems at each iteration of the proposed algorithm we first solve one system of linear equations with a coefficient matrix of size m m where m is the number of constraints to compute the working set we then solve a subproblem which consists of four reduced systems of linear equations with a common coefficient matrix unlike existing qp free algorithms the subproblem is concerned with only the constraints corresponding to the working set the constraints not in the working set are neglected consequently the dimension of each subproblem is not of full dimension without assuming the isolatedness of the stationary points we prove that every accumulation point of the sequence generated by the proposed algorithm is a kkt point of the problem moreover after finitely many iterations the working set becomes independent of the iterates and is essentially the same as the active set of the kkt point in other words after finitely many steps only those constraints which are active at the solution will be involved in the subproblem under some additional conditions we show that the convergence rate is two step superlinear or even q superlinear we also report some preliminary numerical experiments to show that the proposed algorithm is practicable and effective for the test problems

the use of cone shaped kernels for generalized time frequency representations of nonstationary signals generalized time frequency representations gtfrs which use cone shaped kernels for nonstationary signal analysis are presented the cone shaped kernels are formulated for the gtfrs to produce good resolution simultaneously in time and frequency specifically for a gtfr with a cone shaped kernel finite time support is maintained in the time dimension along with an enhanced spectrum in the frequency dimension and the cross terms are smoothed out experimental results on simulated data and real speech show the advantages of the gtfrs with the cone shaped kernels through comparisons to the spectrogram and the pseudo wigner distribution

combined implicit explicit time integration algorithms for the numerical simulation of sheet metal forming in order to simulate stamping processes an explicit method which is conditionally stable is generally thought to be the most adapted such an algorithm presents the advantage of being noniterative while the contact configuration evolves rapidly and the conditional stability is not a disadvantage since time steps must be small enough anyway for an accurate computation but during the springback simulation an implicit method which is iterative presents the advantage of unconditional stability the optimal solution is then to have both implicit and explicit methods readily available in the same code and to be able to switch automatically from one to the other criteria that decide to switch from a method to another depending on the current dynamic have been developed implicit restarting conditions are also proposed that annihilate numerical oscillations resulting from an explicit calculation

tomographic time frequency analysis and its application toward time varying filtering and adaptive kernel design for multicomponent linear fm signals since line integrals through the wigner spectrum can be calculated by dechirping calculation of the wigner spectrum may be viewed as a tomographic reconstruction problem in the paper the authors show that all time frequency transforms of cohen s class may be achieved by simple changes in backprojection reconstruction filtering the resolution cross term tradeoff that occurs in time frequency kernel selection is shown to be analogous to the resolution ringing tradeoff that occurs in computed tomography ct ideal reconstruction using a purely differentiating backprojection filter yields the wigner distribution whereas low pass differentiating filters produce cross term suppressing distributions such as the spectrogram or the born jordan distribution it is also demonstrated how this analogy can be exploited to tune the reconstruction filtering or time frequency kernel to improve the ringing resolution tradeoff some properties of the projection domain which is also known as the radon wigner transform are characterized including the response to signal delays or frequency shifts and projection masking or convolution last time varying filtering by shift varying convolution in the radon wigner domain is shown to yield superior results to its analogous cohen s class adaptive transform shift invariant convolution for the multicomponent linear fm signals that are investigated

eserk5 a fifth order extrapolated stabilized explicit runge kutta method abstract a new algorithm is developed and analyzed for multi dimensional non linear parabolic partial differential equations pdes which are semi discretized in the spatial variables leading to a system of ordinary differential equations odes it is based on fifth order extrapolated stabilized explicit runge kutta schemes eserk they are explicit methods and therefore it is not necessary to employ complicated software for linear or non linear system of equations additionally they have extended stability regions along the negative real semi axis hence they can be considered to solve stiff problems coming from very common diffusion or reaction diffusion problems previously only lower order codes up to fourth order have been constructed and made available in the scientific literature however at the same time higher order codes were demonstrated to be very efficient to solve equations where it is necessary to have a high precision or they have transient zones that are very severe and where functions change very fast the new schemes allow changing the step length very easily and with a very small computational cost thus a variable step length with variable number of stages algorithm is constructed and compared with good numerical results in relation to other well known ode solvers

decomposition of the wigner ville distribution and time frequency distribution series using the orthogonal like gabor expansion the authors decompose the wigner ville distribution wvd to a linear combination of localized and symmetric functions wvd sub h h t w the wvd of the gabor elementary functions h sub m n t and h sub m n t since the influence of the wvd sub h h t w to the useful properties is inversely proportional to the distance between h sub m n t and h sub m n t the wvd sub h h t w are further grouped as a series of the function p sub d t w the authors name the resulting representation the time frequency distribution series tpds also known as the gabor spectrogram in industry the tfdsd consists of up to a dth order p sub d t w while tfds sub 0 t w p sub 0 t w is similar to the spectrogram tfds sub spl infin t w converges to the wvd sub s t w numerical simulations demonstrate that adjusting the order d of the tfds one could effectively balance the cross term interference and the useful properties

improved time frequency representation of multicomponent signals using exponential kernels the authors introduce a time frequency distribution of l cohen s 1966 class and examines its properties this distribution is called exponential distribution ed after its exponential kernel function first the authors interpret the ed from the spectral density estimation point of view they then show how the exponential kernel controls the cross terms as represented in the generalized ambiguity function domain and they analyze the ed for two specific types of multicomponent signals sinusoidal signals and chirp signals next they define the ed for discrete time signals and the running windowed exponential distribution rwed which is computationally efficient finally the authors present numerical examples of the rwed using the synthetically generated signals it is found that the ed is very effective in diminishing the effects of cross terms while retaining most of the properties which are useful for a time frequency distribution

a globally and superlinearly convergent feasible qp free method for nonlinear programming in this paper we propose a qp free type algorithm which solves the problem of minimizing a smooth function subject to smooth inequality constraints in contrast with the sqp methods each iteration this algorithm only needs to solve systems of linear equations which are derived from the equality part in the kkt first order optimality conditions it is observed that if the quasi newton direction is zero we can obtain a direction of descent by dropping a constraint from the active set at the current iterate a high order modified direction is introduced in order to prevent maratos effect global and superlinear convergence are proven under some suitable conditions

a sequential quadratic optimization algorithm with rapid infeasibility detection we present a sequential quadratic optimization sqo algorithm for nonlinear constrained optimization the method attains all of the strong global and fast local convergence guarantees of classical sqo methods but has the important additional feature that fast local convergence is guaranteed when the algorithm is employed to solve infeasible instances a two phase strategy carefully constructed parameter updates and a line search are employed to promote such convergence the first phase subproblem determines the reduction that can be obtained in a local model of an infeasibility measure when the objective function is ignored the second phase subproblem then seeks to minimize a local model of the objective while ensuring that the resulting search direction attains a reduction in the local model of the infeasibility measure that is proportional to that attained in the first phase the subproblem formulations and parameter updates ensure that near an optimal solution the algorithm reduces to a classica

radon transformation of time frequency distributions for analysis of multicomponent signals the radon transform of a time frequency distribution produces local areas of signal concentration that facilitate interpretation of multicomponent signals the radon wigner transform can be efficiently implemented with dechirping in the time domain however only half of the possible projections through the time frequency plane can be realized because of aliasing we show here that the frequency dual to dechirping exists so that all of the time frequency plane projections can be calculated efficiently both time and frequency dechirping are shown to warp the time frequency plane rather rotating it producing an angle dependent dilation of the radon wigner projection axis we derive the discrete time equations for both time and frequency dechirping and highlight some practical implementation issues discrete dechirping is shown to correspond to line integration through the extended discrete rather than the discrete wigner ville distribution computationally dechirping is o 2n log 2n instead of o n sup 3 for direct projection and the computation is dominated by the fast fourier transform calculation the noise and cross term suppression of the radon wigner transform are demonstrated by several examples using dechirping and using direct radon wigner transformation

sharp primal superlinear convergence results for some newtonian methods for constrained optimization as is well known q superlinear or q quadratic convergence of the primal dual sequence generated by an optimization algorithm does not in general imply q superlinear convergence of the primal part primal convergence however is often of particular interest for the sequential quadratic programming sqp algorithm local primal dual quadratic convergence can be established under the assumptions of uniqueness of the lagrange multiplier associated to the solution and the second order sufficient condition at the same time previous primal q superlinear convergence results for sqp required strengthening of the first assumption to the linear independence constraint qualification in this paper we show that this strengthening of assumptions is actually not necessary specifically we show that once primal dual convergence is assumed or already established for primal superlinear rate one needs only a certain error bound estimate this error bound holds for example under the second order sufficient condition which is needed for primal dual local analysis in any case moreover in some situations even second order sufficiency can be relaxed to the weaker assumption that the multiplier in question is noncritical our study is performed for a rather general perturbed sqp framework which covers in addition to sqp and quasi newton sqp some other algorithms as well for example as a byproduct we obtain primal q superlinear convergence results for the linearly constrained augmented lagrangian methods for which no primal q superlinear rate of convergence results were previously available another application of the general framework is sequential quadratically constrained quadratic programming methods finally we discuss some difficulties with proving primal superlinear convergence for the stabilized version of sqp

a robust algorithm for optimization with general equality and inequality constraints an algorithm for general nonlinearly constrained optimization is presented which solves an unconstrained piecewise quadratic subproblem and a quadratic programming subproblem at each iterate the algorithm is robust since it can circumvent the difficulties associated with the possible inconsistency of qp subproblem of the original sqp method moreover the algorithm can converge to a point which satisfies a certain first order necessary optimality condition even when the original problem is itself infeasible which is a feature of burke and han s methods math programming 43 1989 pp 277 303 unlike burke and han s methods our algorithm does not introduce additional bound constraints the algorithm solves the same subproblems as the han powell sqp algorithm at feasible points of the original problem under certain assumptions it is shown that the algorithm coincides with the han powell method when the iterates are sufficiently close to the solution some global convergence results are proved and locally superlinear convergence results are also obtained preliminary numerical results are reported

on the local convergence of quasi newton methods for constrained optimization we consider the application of a general class of quasi newton methods to the solution of the classical equality constrained nonlinear optimization problem specifically we develop necessary and sufficient conditions for the q superlinear convergence of such methods and present a companion linear convergence theorem the essential conditions relate to the manner in which the hessian of the lagrangian function is approximated

self sorting in place fft algorithm with minimum working space presents a modification of temperton s 1991 self sorting in place radix p fft algorithm this modification reduces the required temporary working space from order of p sup 2 to p 1 providing a better match to the limited number of registers in a cpu

fourth order chebyshev methods with recurrence relation in this paper a new family of fourth order chebyshev methods also called stabilized methods is constructed these methods possess nearly optimal stability regions along the negative real axis and a three term recurrence relation the stability properties and the high order make them suitable for large stiff problems often space discretization of parabolic pdes a new code rock4 is proposed illustrated at several examples and compared to existing programs

a second order exponential time differencing scheme for non linear reaction diffusion systems with dimensional splitting abstract a second order l stable exponential time differencing etd method is developed by combining an etd scheme with approximating the matrix exponentials by rational functions having real distinct poles rdp together with a dimensional splitting integrating factor technique a variety of non linear reaction diffusion equations in two and three dimensions with either dirichlet neumann or periodic boundary conditions are solved with this scheme and shown to outperform a variety of other second order implicit explicit schemes an additional performance boost is gained through further use of basic parallelization techniques

stabilized explicit runge kutta methods for multi asset american options american derivatives have become very popular instruments in financial markets however they are more complicated to price than european options since at each time level we have to determine not only the option value but also whether or not it should be exercised several procedures have been proposed to dissolve these difficulties but they usually involve the solution of nonlinear partial differential equations pdes in the case of multi dimensional problems solving these equations is a very challenging task in this paper we propose stabilized explicit runge kutta serk methods to solve this kind of problems they can easily be applied to many different classes of problems with large dimensions and they have low memory demand since these methods are explicit they do not require algebra routines to solve large nonlinear systems associated to odes as for example lapack and blas packages or multigrid or iterative methods applied together with newton type algorithms and are especially well suited for the method of lines mol discretizations of parabolic pdes

frequency evaluation in exponential fitting multistep algorithms for odes we consider the linear multistep algorithms for first order odes and examine the problem of how the frequencies should be tuned in order to obtain the maximal benefit from the exponential fitting versions of such algorithms we find out that the key of the answer consists in analysing the behaviour of the error on further investigating the simple case of two step bdf algorithms we produce formulae for the optimal s and show that if the optimal s are used the order of the method is increased by one unit the reported numerical illustrations suggest that further investigations along these lines deserve a real attention

fixed point quasi newton methods this article studies iterative methods defined by x k 1 phi x k e k where x k in mathbb r n and e k lie on a space of parameters sufficient conditions are established for local convergence and for convergence at an ideal linear or superlinear rate a theory of least change secant update methods for this class of processes is developed several examples are given showing a wide range of applications of the new theory key words quasi

rkc an explicit solver for parabolic pdes the fortran program rkc is intended for the time integration of parabolic partial differential equations discretized by the method of lines it is based on a family of runge kutta chebyshev formulas with a stability bound that is quadratic in the number of stages remarkable properties of the family make it possible for the program to select at each step the most efficient stable formula as well as the most efficient step size moreover they make it possible to evaluate the explicit formulas in just a few vectors of storage these characteristics of the program make it especially attractive for problems in several spatial variables rkc is compared to the bdf solver vodpk on two test problems in three spatial variables

the locally extrapolated exponential time differencing lod scheme for multidimensional reaction diffusion systems this paper introduces the local extrapolation of first order locally one dimensional exponential time differencing scheme for numerical solution of multidimensional nonlinear reaction diffusion systems this novel scheme has the benefit of solving multidimensional problems in locally one dimensional fashion by implementing sequences of tridiagonal matrix solvers instead of solving a banded system the storage size needed for solving systems in higher dimensions with this scheme is similar to that needed for one spatial dimension systems the stability monotonicity and convergence of the locally extrapolated exponential time differencing scheme have been examined stability analysis shows that the scheme is strongly stable l stable and is particularly beneficial to nonlinear partial differential equations with irregular initial data or discontinuity involving initial and boundary conditions due to its ability to damp spurious oscillations caused by high frequency components in the solution the performance of the novel scheme has been investigated by testing it on a two dimensional schnakenberg model two and three dimensional brusselator models and a three dimensional enzyme kinetics of michaelis menten type reaction diffusion model numerical experiments demonstrate the efficiency accuracy and reliability of the scheme locally extrapolated lod exponential time differencing scheme is developed multidimensional nonlinear reaction diffusion systems are considered monotonicity and stability are analyzed the order of convergence is examined

a type of efficient feasible sqp algorithms for inequality constrained optimization in this paper motivated by zhu et al methods z b zhu k c zhang j b jian an improved sqp algorithm for inequality constrained optimization math meth oper res 58 2003 271 282 zhibin zhu jinbao jian an efficient feasible sqp algorithm for inequality constrained optimization nonlinear anal real world appl 10 2 2009 1220 1228 we propose a type of efficient feasible sqp algorithms to solve nonlinear inequality constrained optimization problems by solving only one qp subproblem with a subset of the constraints estimated as active a class of revised feasible descent directions are generated per single iteration these methods are implementable and globally convergent we also prove that the algorithms have superlinear convergence rate under some mild conditions