iterative time limited signal restoration the purpose of this paper is to show that time limited restoration of shift invariant blurred signals can be done by means of fixed point solutions of contraction mappings under rather general conditions for the distortion operator all our results are valid for multidimensional signals an application of these results to the iterative extrapolation of band limited discrete images is shown

error analysis of a class of constrained iterative restoration algorithms in this paper we investigate the problem of noise stability in a class of iterative image restoration algorithms the algorithm is a gerchberg papoulis type algorithm that utilizes incomplete information and partial constraints to specify constraint operators for the iteration the iteration in the absence of noise converges to a unique solution in the presence of noise the restoration is considered as an ill posed problem in this study noise stability of the algorithm is investigated a general error analysis method is derived to predict the optimum number of iterations that minimizes the mean square error between the ideal and the restored image the tradeoff between signal reconstruction and noise amplification has been investigated and it has been shown that by using prior knowledge of the signal and noise statistics it is possible to achieve optimal restoration simulations have been performed to verify the theoretical results

a conservative fourier pseudo spectral method for the nonlinear schrodinger equation a fourier pseudo spectral method that conserves mass and energy is developed for a two dimensional nonlinear schrodinger equation by establishing the equivalence between the semi norm in the fourier pseudo spectral method and that in the finite difference method we are able to extend the result in ref 56 to prove that the optimal rate of convergence of the new method is in the order of o n r 2 in the discrete l 2 norm without any restrictions on the grid ratio where n is the number of modes used in the spectral method and is the time step size a fast solver is then applied to the discrete nonlinear equation system to speed up the numerical computation for the high order method numerical examples are presented to show the efficiency and accuracy of the new method

a canonical transformation relating the lagrangian and eulerian description of ideal hydrodynamics abstract we derive by means of a canonical transformation the variational principle of seliger and whitham for the eulerian description of ideal hydrodynamics from the more familiar variational principle that yields the equations of motion of an ideal fluid in the lagrangian description

linear pdes and numerical methods that preserve a multisymplectic conservation law multisymplectic methods have recently been proposed as a generalization of symplectic ode methods to the case of hamiltonian pdes their excellent long time behavior for a variety of hamiltonian wave equations has been demonstrated in a number of numerical studies a theoretical investigation and justification of multisymplectic methods is still largely missing in this paper we study linear multisymplectic pdes and their discretization by means of numerical dispersion relations it is found that multisymplectic methods in the sense of bridges and reich phys lett a 284 2001 pp 184 193 and reich j comput phys 157 2000 pp 473 499 such as gauss legendre runge kutta methods possess a number of desirable properties such as nonexistence of spurious roots and conservation of the sign of the group velocity a certain cfl type restriction on delta t delta x might be required for methods higher than second order in time it is also demonstrated by means of the explicit midpoint method that multistep methods may exhibit spurious roots in the numerical dispersion relation for any value of delta t delta x despite being multisymplectic in the sense of discrete variational mechanics j e marsden g p patrick and s shkoller commun math phys 199 1999 pp 351 395

rounding effects of quenched randomness on first order phase transitions frozen in disorder in an otherwise homogeneous system is modeled by interaction terms with random coefficients given by independent random variables with a translation invariant distribution for such systems it is proven that ind 2 dimensions there can be no first order phase transition associated with discontinuities in the thermal average of a quantity coupled to the randomized parameter discontinuities which would amount to a continuous symmetry breaking in systems which are stochastically invariant under the action of a continuous subgroup ofo n are suppressed by the randomness in dimensionsd 4 specific implications are found in the random field ising model for which we conclude that ind 2 dimensions at all h the gibbs state is unique for almost all field configurations and in the random bond potts model where the general phenomenon is manifested in the vanishing of the latent heat at the transition point the results are explained by the argument of imry and ma 1 the proofs involve the analysis of fluctuations of free energy differences which are shown using martingale techniques to be gaussian on the suitable scale

regularized iterative image restoration with ringing reduction linear space invariant image restoration algorithms often introduce ringing effects near sharp intensity transitions it is shown that these artifacts are attributable to the regularization of the ill posed image restoration problem two possible methods to reduce the ringing effects in restored images are proposed the first method incorporates deterministic a priori knowledge about the original image into the restoration algorithm the second method locally regulates the severity of the noise magnification and the ringing phenomenon depending on the edge information in the image a regularized iterative image restoration algorithm is proposed in which both ringing reduction methods are included by making use of the theory of the projections onto convex sets and the concept of norms in a weighted hilbert space both the numerical performance and the visual evaluation of the results are improved by the use of ringing reduction

an energy preserving crank nicolson galerkin spectral element method for the two dimensional nonlinear schrodinger equation abstract a crank nicolson galerkin spectral element method for solving the nonlinear schrodinger nls equation in two dimensions is proposed in this paper our key idea is twofolds first the 2d nls equation is rewritten as an infinite dimensional hamiltonian pde and the hamiltonian pde is discreted by using the galerkin spectral element gse method in space second we cast the resulted odes into a finite dimensional canonical hamiltonian system and discrete the system by using the crank nicolson cn method the relay leads to a fully discretized and energy preserved scheme without grid ratio restrictions the order of convergence of our new method is o 2 h 2 if the discrete l 2 norm is employed the fast fourier transform and the matrix diagonalization method are applied to the new method to increase computing efficiency numerical examples are given to further illustrate the conservation properties and convergence of the energy preserving scheme constructed

image representation by one bit fourier phase theory sampling and coherent image model the problem of recovering an image from its fourier transform phase quantized to one bit or equivalently finding the locations of the zero crossings of the real part of the fourier transform is addressed theoretical results are presented that set an algebraic condition under which real zero crossings uniquely specify a band limited image it is then shown that sampling in the frequency domain presents a major obstacle to obtaining good reconstruction results the one bit fourier phase reconstruction problem is then considered when the original image is coherent i e the image phase is random and highly uncorrelated examples are given which demonstrate that the information loss produced by frequency sampling is not as severe as that in the nonclassical problem motivated by digital phase only holograms a known random diffuser is used as the image phase and a well known iterative reconstruction procedure is extended to incorporate the knowledge of the image phase at each stage of the iteration this reconstruction method produces good image quality by using a few iterations unlike its noncoherent counterpart

the reconstruction of a multidimensional sequence from the phase or magnitude of its fourier transform this paper addresses two fundamental issues involved in the reconstruction of a multidimensional sequence from either the phase or magnitude of its fourier transform the first issue relates to the uniqueness of a multidimensional sequence in terms of its phase or magnitude although phase or magnitude information alone is not sufficient in general to uniquely specify a sequence a large class of sequences are shown to be recoverable from their phase or magnitude the second issue which is addressed in this paper concerns the actual reconstruction of a multidimensional sequence from its phase or magnitude for those sequences which are uniquely specified by their phase several practical algorithms are described which may be used to reconstruct a sequence from its phase several examples of phase only reconstruction are also presented unfortunately however even for those sequences which are uniquely defined by their magnitude it appears that a practical algorithm is yet to be developed for reconstructing a sequence from only its magnitude nevertheless an iterative procedure which has been proposed is briefly discussed and evaluated

signal reconstruction from the phase of the bispectrum the authors present a simple procedure the bispectrum signal reconstruction bsr algorithm to recover the fourier phase of a signal from the phase of its bispectrum by simple analogy a procedure that recovers the fourier magnitude of a signal from the magnitude of its bispectrum is also presented in addition the authors propose an iterative scheme the bicepstrum iterative reconstruction algorithm bira for the reconstruction of a finite impulse response fir sequence from only the phase of its bispectrum and they demonstrate how some a priori information on the energy of the cepstra coefficients can improve significantly the convergence rate of the algorithm both schemes are based on the key observation that the differences of the bispectrum coefficients contain all the information concerning the fourier phase of the signal whereas their sums contain the fourier magnitude information

two classes of linearly implicit local energy preserving approach for general multi symplectic hamiltonian pdes abstract two classes of efficient and robust schemes are proposed for the general multi symplectic hamiltonian systems using the invariant energy quadratization ieq approach the schemes are linear second order accurate local energy preserving and preserve the global energy they are not restricted to specific forms of the nonlinear part of the state function and only require solving linear equations at each time step we applied the new schemes to various multi symplectic hamiltonian pdes to demonstrate their effectiveness computational efficiency and accuracy

fast reconstruction of linearly distorted signals a product expansion of the inverse operator is used to derive a class of iterative algorithms that have a pth order rate of convergence compared to the linear algorithm the number of iterations required to obtain a given reconstruction is reduced from p sup n to n the primary difference between these algorithms and the linear algorithm is that they update both the estimate of x and the operator d rather than the estimate alone several methods that may be used to incorporate linear and nonlinear constraints are also proposed finally some examples of linear inverse problems are presented and the differences in rates of convergence for the linear and the pth order algorithms are compared

on the mean field ising model in a random external field we use a method developed by van hemmen to obtain the free energy of the mean field ising model in a random external magnetic field some results of previous mean field calculations are confirmed and generalized the tricritical point in the global phase diagram is discussed in detail we also consider different probability distributions of the random fields and provide some proofs regarding the conditions for the existence of a tricritical point

multi symplectic runge kutta collocation methods for hamiltonian wave equations a number of conservative pdes like various wave equations allow for a multi symplectic formulation which can be viewed as a generalization of the symplectic structure of hamiltonian odes we show that gauss legendre collocation in space and time leads to multi symplectic integrators i e to numerical methods that preserve a symplectic conservation law similar to the conservation of symplecticity under a symplectic method for hamiltonian odes we also discuss the issue of conservation of energy and momentum since time discretization by a gauss legendre method is computational rather expensive we suggest several semi explicit multi symplectic methods based on gauss legendre collocation in space and explicit or linearly implicit symplectic discretizations in time

some aspects of band limited signal extrapolation models discrete approximations and noise we present some theoretical results on the band limited signal extrapolation problem in section i we describe four basic models for the extrapolation problem these models are useful in understanding the relationship between the continuous extrapolation problem and some discrete algorithms given in 1 and 2 one of these models was shown to approximate the continuous band limited extrapolation problem 3 another model is obtained when the discrete fourier transform dft is used to implement the well known iterative algorithm given in 4 and 5 which was designed for solving the continuous extrapolation problem in section ii this model is related to the continuous model by means of an interesting approximation theorem also an important conjecture is presented section iii shows some approximation results specifically we prove that some discrete discrete and discrete continuous extrapolations of noisy signals converge to solutions of a certain continuous continuous noisy extrapolation problem when the noise is bounded by a known number max eta x leq epsilon this convergence is obtained by using normal families of entire functions in nand some other complex analysis tools we also show that the extrapolation problem is very sensitive to noise even in cases where only small amounts of extrapolation are desired this result indicates that in the presence of noise extrapolation techniques should be used judiciously in order to obtain reasonable results

algorithmic framework for group analysis of differential equations and its application to generalized zakharov kuznetsov equations abstract in this paper we explain in more details the modern treatment of the problem of group classification of systems of partial differential equations pdes from the algorithmic point of view more precisely we revise the classical lie algorithm of construction of symmetries of differential equations describe the group classification algorithm and discuss the process of reduction of systems of pdes to systems of equations with smaller number of independent variables in order to construct invariant solutions the group classification algorithm and reduction process are illustrated by the example of the generalized zakharov kuznetsov gzk equations of form u t f u x x x g u x y y h u x 0 as a result a complete group classification of the gzk equations is performed and a number of new interesting nonlinear invariant models which have non trivial invariance algebras are obtained lie symmetry reductions and exact solutions for two important invariant models i e the classical and modified zakharov kuznetsov equations are constructed the algorithmic framework for group analysis of differential equations presented in this paper can also be applied to other nonlinear pdes

a new extrapolation algorithm for band limited signals using the regularization method the ill posedness of the extrapolation problem in the presence of noise is considered a stable algorithm is constructed by solving a fredholm equation based on a regularization method the algorithm appears relatively robust since the noise eta sub delta t is taken as a function in l sup 2 t t t 0 such that the error energy integral mod eta sub delta t mod sup 2 dt

multisymplectic geometry local conservation laws and fourier pseudospectral discretization for the good boussinesq equation the multisymplectic geometry for the good boussinesq equation is presented in this paper the multisymplectic form and the local energy and momentum conservation laws are derived directly from the variational principle the multisymplectic hamiltonian formulation is also presented based on the multisymplectic formulation we investigate the corresponding multisymplectic fourier pseudospectral discretization

an algorithm to find two dimensional signals with specified zero crossings we present an iterative method for finding two dimensional band limited functions with predetermined zero crossings this problem arises when we want to generate a prescribed binary image at the output of a diffraction limited imaging system with high contract recording an important application of this image generation problem is in the design of masks for microlithography after describing the algorithm a proof of its convergence based on the properties of nonexpansive mappings is given the relevance of this algorithm to the image construction problem is then discussed and we conclude by illustrating two patterns generated by our proposed method

multisymplectic geometry variational integrators and nonlinear pdes this paper presents a geometric variational approach to continuous and discrete mechanics and field theories using multisymplectic geometry we show that the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the variational principle in particular we prove that a unique multisymplectic structure is obtained by taking the derivative of an action function and use this structure to prove covariant generalizations of conservation of symplecticity and noether s theorem natural discretization schemes for pdes which have these important preservation properties then follow by choosing a discrete action functional in the case of mechanics we recover the variational symplectic integrators of veselov type while for pdes we obtain covariant spacetime integrators which conserve the corresponding discrete multisymplectic form as well as the discrete momentum mappings corresponding to symmetries we show that the usual notion of symplecticity along an infinite dimensional space of fields can be naturally obtained by making a spacetime split all of the aspects of our method are demonstrated with a nonlinear sine gordon equation including computational results and a comparison with other discretization schemes

a multisymplectic pseudospectral method for seismic modeling seismic modeling is a foundation of geophysical date processing a multisymplectic pseudospectral method for seismic modeling is presented in this paper this method takes the multisymplectic structure of the scalar wave equation into account and possesses discrete multisymplectic conservation laws numerical experiments demonstrate the remarkable capability of this new method for long time simulations

dilute antiferromagnets imry ma argument hierarchical model and equivalence to random field ising models we discuss some aspects of the problem of the equivalence of dilute antiferromagnets and random field ising models we first investigate for dilute antiferromagnets the validity of the arguments of imry and ma it turns out that they are applicable but some care is required concerning the role played by the so called internal peierls contours next we consider a hierarchical version of a dilute antiferromagnetic ising model in the presence of a uniform magnetic field and show that a renormalization group transformation maps it exactly into a hierarchical version of the random field ising model thus proving their equivalence as far as the critical behavior is concerned in particular this implies that phase transition with spontaneous magnetization occurs only for dimensiond 2 finally we show that in the absence of internal peierls contours both models in their hierarchical versions exhibit phase transition already in dimensiond 2

a note on iterative fourier transform phase reconstruction from magnitude in this correspondence a well known iterative procedure for fourier transform phase reconstruction from magnitude usually referred to as the gerchberg saxton fienup procedure is revisited the convergence of this algorithm has raised some controversy in the recent literature in this correspondence we first point out a potential source of error in the numerical implementation of the algorithm then we present a conjecture which would explain why this algorithm sometimes fails

cylindrical quasi solitons of the zakharov kuznetsov equation abstract evolutions and interactions of two dimensional solitary waves of the zakharov kuznetsov equation are investigated numerically formations of cylindrical bell shaped pulses are observed in the initial value problems a single bell shaped pulse propagates stably without any deformation like a soliton two similar pulses exchange their amplitudes without merging and two dissimilar ones undergo overtaking collision after a collision of two pulses the strong pulse becomes somewhat stronger and the weak one becomes weaker with radiation of ripples so that the collision process is slightly inelastic generated ripples are very small for center to center collision of similar pulses the cylindrically symmetric pulses of the zakharov kuznetov equation are thus found to behave approximately soliton like some properties of collision process are interpreted in terms of the conservation laws

on the preservation of phase space structure under multisymplectic discretization in this paper we explore the local and global properties of multisymplectic discretizations based on finite differences and fourier spectral approximations multisymplectic ms schemes are developed for two benchmark nonlinear wave equations the sine gordon and nonlinear schrodinger equations we examine the implications of preserving the ms structure under discretization on the numerical scheme s ability to preserve phase space structure as measured by the nonlinear spectrum of the governing equation we find that the benefits of multisymplectic integrators include improved resolution of the local conservation laws dynamical invariants and complicated phase space structures

optimal error estimate of a linear fourier pseudo spectral scheme for two dimensional klein gordon schrodinger equations abstract the focus of this paper is on the optimal error bounds of a fourier pseudo spectral conservative scheme for solving the 2 dimensional nonlinear klein gordon schrodinger equations the proposed fourier pseudo spectral scheme not only conserves the mass and energy in the discrete level but also is efficient in practical computation because only two linear systems need to be solved at each time step based on the equivalence between the semi norm derived by the fourier pseudo spectral method and that by the finite difference method the pseudo spectral solution of the proposed scheme is proved strictly to be bounded and convergent with the order of o n r 2 in the discrete l 2 norm where n is the number of nodes and is the time step size some numerical experiments are carried out to validate the theoretical analysis

on nonparaxial nonlinear schrodinger type equations abstract in this paper the one dimensional nonparaxial nonlinear schrodinger equation is considered this was proposed as an alternative to the classical nonlinear schrodinger equation in those situations where the assumption of paraxiality may fail the paper contributes to the mathematical properties of the equation in a two fold way first some theoretical results on linear well posedness hamiltonian and multi symplectic formulations are derived then we propose to take into account these properties in order to deal with the numerical approximation in this sense different numerical procedures that preserve the hamiltonian and multi symplectic structures are discussed and illustrated with numerical experiments

multi symplectic methods for the ito type coupled kdv equation abstract in this paper we find that the ito type coupled kdv equation can be written as a multi symplectic hamiltonian partial differential equation pde then multi symplectic fourier pseudospectral method and multi symlpectic wavelet collocation method are constructed for this equation in the numerical experiments we show the effectiveness of the proposed methods some comparisons between the proposed methods are also made with respect to global conservation properties

numerical methods for hamiltonian pdes the paper provides an introduction and survey of conservative discretization methods for hamiltonian partial differential equations the emphasis is on variational symplectic and multi symplectic methods the derivation of methods as well as some of their fundamental geometric properties are discussed basic principles are illustrated by means of examples from wave and fluid dynamics

iterative techniques for minimum phase signal reconstruction from phase or magnitude in this paper we develop iterative algorithms for reconstructing a minimum phase sequence from the phase or magnitude of its fourier transform these iterative solutions involve repeatedly imposing a causality constraint in the time domain and incorporating the known phase or magnitude function in the frequency domain this approach is the basis of a new means of computing the hilbert transform of the log magnitude or phase of the fourier transform of a minimum phase sequence which does not require phase unwrapping finally we discuss the potential use of this iterative computation in determining samples of the unwrapped phase of a mixed phase sequence

on multisymplecticity of sinc gauss legendre collocation discretizations for some hamiltonian pdes abstract in this paper a new multisymplectic scheme based on sinc collocation discretization in space and gauss legendre collocation discretization in time for some hamiltonian pdes is developed the scheme preserves the multisymplectic geometry structure exactly by satisfying the discrete multisymplectic conservation law moreover the discrete energy and momentum conservative properties of the multisymplectic integrator are also discussed in order to testify the superiority of the multisymplectic method it is applied to nonlinear dirac equation numerical experiments are given to illustrate the accuracy of the approximation and the conserved quantities

iterative least squares estimators in nonlinear image restoration the concept of iterative least squares estimation as applied to nonlinear image restoration is considered regarding the convergence analysis of nonlinear iterative algorithms the potential of the global convergence theorem gct is explored the theoretical analysis is performed on a general class of nonlinear algorithms which defines a signal dependent linear mapping of the residual the descent properties of two normed functions are considered furthermore a procedure for the selection of the iteration parameter is introduced the steepest descent sd iterative approach for the solution of the least squares optimization problem is introduced the convergence properties of the particular algorithm are readily derived on the basis of the generalized analysis and the gct the factors that affect the convergence rate of the sd algorithm are thoroughly studied in the case of the sd algorithm structural modifications are proposed and two hybrid sd algorithms attain convergence in a more uniform fashion with respect to their entries in general the algorithms achieve larger convergence rates than the conventional sd technique

phase transition in the 3d random field ising model we show that the three dimensional ising model coupled to a small random magnetic field is ordered at low temperatures this means that the lower critical dimension dl for the theory isdl 2 settling a long controversy on the subject our proof is based on an exact renormalization group rg analysis of the system this analysis is carried out in the domain wall representation of the system and it is inspired by the scaling arguments of imry and ma the rg acts in the space of ising models and in the space of random field distributions driving the former to zero temperature and the latter to zero variance

generalized multi symplectic integrators for a class of hamiltonian nonlinear wave pdes nonlinear wave equations such as burgers equation and compound kdv burgers equation are a class of partial differential equations pdes with dissipation in hamiltonian space the numerical method of which plays an important role in complex fluid analysis based on the multi symplectic idea a new theoretical framework named generalized multi symplectic integrator for a class of nonlinear wave pdes with small damping is proposed in this paper the generalized multi symplectic formulation is introduced and a twelve point generalized multi symplectic scheme which satisfies two discrete modified conservation laws approximately as well as the local momentum conservation law accurately is constructed to solve the first order pdes that derived from the compound kdv burgers equation to test the generalized multi symplectic scheme several numerical experiments on the travelling front solution are carried out the results of which imply that the generalized multi symplectic scheme can simulate the travelling front solution accurately and satisfy the modified conservation laws well when step sizes and the damping parameter satisfy the inequality 41 it is more remarkable that the scheme 36 can be used to capture the shock wave structure of the compound kdv burgers equation within one data point which can further illustrate the good structure preserving property of the generalized multi symplectic scheme 36 from the results of this paper we can conclude that similar to the multi symplectic scheme the generalized multi symplectic scheme also has two remarkable advantages the excellent long time numerical behavior and the good conservation property for the existing of the excellent numerical properties the generalized multi symplectic method can be used to exposit some specific phenomena in the complex fluid

fluctuations in dilute antiferromagnets curie weiss models the authors compute the fluctuations of the order parameter in the curie weiss version of a site dilute antiferromagnet their results show i gaussian fluctuations away from criticality or at a first order critical point with sample and thermal fluctuations contributing in same order ii non gaussian fluctuations with critical exponents modified by the presence of dilution at the second order critical point in this case sample induced fluctuations are enhanced to dominate over the thermal ones critical exponents are the same as in the curie weiss random field ising model

the multi symplectic fourier pseudospectral method for solving two dimensional hamiltonian pdes in this paper the multi symplectic fourier pseudospectral msfp method is generalized to solve two dimensional hamiltonian pdes with periodic boundary conditions using the fourier pseudospectral method in the space of the two dimensional hamiltonian pde 2d hpde the semi discrete system obtained is proved to have semi discrete multi symplectic conservation laws and a global symplecticity conservation law then the implicit midpoint rule is employed for time integration to obtain the msfp method for the 2d hpde the fully discrete multi symplectic conservation laws are also obtained in addition the proposed method is applied to solve the zakharov kuznetsov zk equation and the kadomtsev petviashvili kp equation numerical experiments on soliton solutions of the zk equation and the kp equation show the high accuracy and effectiveness of the proposed method

the lu decomposition theorem and its implications to the realization of two dimensional digital filters a new approach to the realization of two dimensional 2 d fir and iir digital filters is introduced based on the so called lower upper triangular lu decomposition of matrix coefficients of their two dimensional polynomials it is demonstrated that the lu realization scheme enjoys a number of attributes for vlsi implementation including high parallelism modularity and regularity this paper also shows that the computational requirements of the lu realization structure are much smaller than those of the jordan jd singular value sv and canonical direct realizations furthermore it is shown that if a canonical 2 d iir filter is realizable then a realizable lu decomposition form can be always obtained a property that is not shared by the jd and sv decomposition forms finally the extension of the lu decomposition approach to the realization of m d digital filters is discussed

multitone signals with low crest factor after an introductory discussion of real valued and complex signals it is shown that minimizing the crest factor cf of multitone signals is closely related to the construction of complex sequences with low sidelobes in their aperiodic autocorrelation function inspired by this observation a lower bound on the achievable cf is derived four differing algorithms for the reduction of the cf of complex multitone signals are compared with each other by computer simulation the preferred algorithm is presented in detail and its convergence is proven examples of multitone signals with up to 15 tones and lower cf than previously reported in the literature are given

a survey on symplectic and multi symplectic algorithms we simply review symplectic and multi symplectic algorithms in the paper these algorithms have many superiorities to general non symplectic algorithms such as they have long time behavior they can preserve the symplectic geometry structure of the hamiltonian system exactly and they can simulate original physical phenomena well some commonly used methods to construct symplectic and multi symplectic schemes are simply surveyed numerical examples are also enumerated to illustrate their performances

energy conservation issues in the numerical solution of the semilinear wave equation in this paper we discuss energy conservation issues related to the numerical solution of the semilinear wave equation as is well known this problem can be cast as a hamiltonian system that may be autonomous or not depending on the prescribed boundary conditions we relate the conservation properties of the original problem to those of its semi discrete version obtained by the method of lines subsequently we show that the very same properties can be transferred to the solutions of the fully discretized problem obtained by using energy conserving methods in the hbvms hamiltonian boundary value methods class similar arguments hold true for different types of hamiltonian partial differential equations e g the nonlinear schrodinger equation

a note on multisymplectic fourier pseudospectral discretization for the nonlinear schrodinger equation based on the multisymplectic fourier pseudospectral scheme for the nonlinear schrodinger nls equation we investigate some discrete properties corresponding to local conservation laws of the original equation the discrete normal conservation law is proved and the error estimation of local and global energy conservation laws are also obtained numerical experiments for cubic nls equation are provided to demonstrate the consistency between the theoretical analysis and the numerical results

multi symplectic quasi interpolation method for hamiltonian partial differential equations abstract in this paper we propose a multi symplectic quasi interpolation method for solving multi symplectic hamiltonian partial differential equations based on the method of lines we first discretize the multi symplectic pdes using quasi interpolation method and then employ appropriate time integrators to obtain the full discrete system the local conservation properties including multi symplectic conservation laws energy conservation laws and momentum conservation laws are discussed in detail for illustration we provide two concrete examples the nonlinear wave equation and the nonlinear schrodinger equation the salient feature of our multi symplectic quasi interpolation method is that it is valid both on uniform grids and nonuniform grids the numerical results show the good accuracy and excellent conservation properties of the proposed method

estimation of linear parametric models of nongaussian discrete random fields with application to texture synthesis a general possibly asymmetric noncausal and or nonminimum phase 2d autoregressive moving average random field model driven by an independent and identically distributed 2d nongaussian sequence is considered the model is restricted to be invertible i e system zeros are not allowed to lie on the unit bicircle three performance criteria are investigated for parameter estimation of the system parameters given only the output measurements image pixels the proposed criteria are functions of the higher order cumulant statistics of an inverse filter output one of these criteria is novel and the others have been considered in past only for moving average inverses and without any analysis of their consistency in the paper strong consistency of the proposed methods under the assumption that the system order is known is proved the convergence of the proposed parameter estimators under overparametrization is also analyzed experimental results involving synthesized as well as real life textures are presented to illustrate the performance of two of the considered approaches experimental results of synthesis of 128 spl times 128 textures visually resembling several real life textures in the brodatz album and other sources are presented

on the duality of time and frequency domain signal reconstruction from partial information certain results on one dimensional signal representation and reconstruction from partial information in the frequency domain are related to and derived using relevant results obtained in the time or positional information domain in particular we adopt logan s approach and apply his results concerning zero crossing representation of certain bandpass signals we also apply voelcker s results on demodulation of analytic ssb signals by an am detector exploiting the duality of the fourier stieltjes transform and its inverse we rederive and extend to continuous one dimensional signals some results concerning the representation of fourier transformed discrete time finite sequences by partial information such as one bit or complete fourier phase fourier magnitude or signed magnitude the duality and interrelationship of characteristics and constraints attributed to time and frequency signal representation create further possibilities of drawing results and interpretations from one to its counter domain in particular we indicate possible extensions of certain results to problems of n dimensional signals and to issues of stochastic signals we also highlight basic issues concerning the structure of signals and their reconstruction from partial information

explicit multi symplectic methods for klein gordon schrodinger equations in this paper we propose explicit multi symplectic schemes for klein gordon schrodinger equation by concatenating suitable symplectic runge kutta type methods and symplectic runge kutta nystrom type methods for discretizing every partial derivative in each sub equation it is further shown that methods constructed in this way are multi symplectic and preserve exactly the discrete charge conservation law provided appropriate boundary conditions in the aim of the commonly practical applications a novel 2 order one parameter family of explicit multi symplectic schemes through such concatenation is constructed and the numerous numerical experiments and comparisons are presented to show the efficiency and some advantages of the our newly derived methods furthermore some high order explicit multi symplectic schemes of such category are given as well good performances and efficiencies and some significant advantages for preserving the important invariants are investigated by means of numerical experiments

interpolation and the discrete papoulis gerchberg algorithm analyze the performance of an iterative algorithm similar to the discrete papoulis gerchberg algorithm and which can be used to recover missing samples in finite length records of band limited data no assumptions are made regarding the distribution of the missing samples in contrast with the often studied extrapolation problem in which the known samples are grouped together indeed it is possible to regard the observed signal as a sampled version of the original one and to interpret the reconstruction result studied as a sampling result the authors show that the iterative algorithm converges if the density of the sampling set exceeds a certain minimum value which naturally increases with the bandwidth of the data they give upper and lower bounds for the error as a function of the number of iterations together with the signals for which the bounds are attained also they analyze the effect of a relaxation constant present in the algorithm on the spectral radius of the iteration matrix from this analysis they infer the optimum value of the relaxation constant they also point out among all sampling sets with the same density those for which the convergence rate of the recovery algorithm is maximum or minimum for low pass signals it turns out that the best convergence rates result when the distances among the missing samples are a multiple of a certain integer the worst convergence rates generally occur when the missing samples are contiguous

multi symplectic spectral discretizations for the zakharov kuznetsov and shallow water equations abstract the time evolution of multi symplectic pdes with periodic boundary conditions in one and two space dimensions is considered we introduce the idea of a multi symplectic fourier transform for systems on periodic domains leading to a semi discretization on fourier space and to the concept of multi symplecticity on fourier space the spatial discretization leads to a discrete lattice model with certain discrete conservation laws imposed on it a discrete wave model a by product of the semi discretization is that it leads automatically to a system of hamiltonian odes in time when truncated we show that the one dimensional shallow water equations and the two dimensional zakharov kuznetsov equation are multi symplectic and derive spectral discretizations for these systems and present numerical experiments

general local energy preserving integrators for solving multi symplectic hamiltonian pdes in this paper we propose and investigate a general approach to constructing local energy preserving algorithms which can be of arbitrarily high order in time for solving hamiltonian pdes this approach is based on the temporal discretization using continuous runge kutta type methods and the spatial discretization using pseudospectral methods or gauss legendre collocation methods the local energy conservation law of our new schemes is analyzed in detail the effectiveness of the novel local energy preserving integrators is demonstrated by coupled nonlinear schrodinger equations and 2d nonlinear schrodinger equations with external fields our new schemes are compared with some classical multi symplectic and symplectic schemes in numerical experiments the numerical results show the remarkable long term behaviour of our new schemes

conservation laws of semidiscrete canonical hamiltonian equations there are many evolution partial differential equations which can be cast into hamiltonian form conservation laws of these equations are related to one parameter hamiltonian symmetries admitted by the pdes the same result holds for semidiscrete hamiltonian equations in this paper we consider semidiscrete canonical hamiltonian equations using symmetries we find conservation laws for the semidiscretized nonlinear wave equation and schrodinger equation

convergence of iterative nonexpansive signal reconstruction algorithms iterative algorithms for signal reconstruction from partial time and frequency domain knowledge have proven useful in a number of application areas in this paper a general convergence proof applicable to a general class of such iterative reconstruction algorithms is presented the proof relies on the concept of a nonexpansive mapping in both the time and frequency domains two examples studied in detail are time limited extrapolation equivalently band limited extrapolation and phase only signal reconstruction the proof of convergence for the phase only iteration is a new result obtained by this method of proof the generality of the approach allows the incorporation of nonlinear constraints such as time or space domain positivity or minimum and maximum value constraints finally the underrelaxed form of these iterations is also shown to converge even when the solution is not guaranteed to be unique

on structure preserving discontinuous galerkin methods for hamiltonian partial differential equations energy conservation and multi symplecticity abstract in this paper we present and study discontinuous galerkin dg methods for one dimensional multi symplectic hamiltonian partial differential equations we particularly focus on semi discrete schemes with spatial discretization only and show that the proposed dg methods can simultaneously preserve the multi symplectic structure and energy conservation with a general class of numerical fluxes which includes the well known central and alternating fluxes applications to the wave equation the benjamin bona mahony equation the camassa holm equation the korteweg de vries equation and the nonlinear schrodinger equation are discussed some numerical results are provided to demonstrate the accuracy and long time behavior of the proposed methods numerically we observe that certain choices of numerical fluxes in the discussed class may help achieve better accuracy compared with the commonly used ones including the central fluxes

error estimates of exponential wave integrator fourier pseudospectral methods for the nonlinear schrodinger equation abstract in this article several exponential wave integrator fourier pseudospectra methods are developed for solving the nonlinear schrodinger equation in two dimensions these numerical methods are based on the fourier pseudospectral discretization for spatial derivative first and then utilizing four types of numerical integration formulas including the gautschi type trapezoidal middle rectangle and simpson rules to approximate the time integral in phase space the resulting numerical methods cover two explicit and an implicit schemes and can be implemented effectively thanks to the fast discrete fourier transform additionally the error estimates of two explicit schemes are established by virtue of the mathematical induction and standard energy method finally extensive numerical results are reported to show the efficiency and accuracy of the proposed new methods and confirm our theoretical analysis

reconstruction of signals from phase efficient algorithms segmentation and generalizations in this paper we develop several new formulations of the phase only reconstruction problem which lead to new efficient algorithms for signal reconstruction we describe a procedure for approximately reconstructing a long duration signal from short segments phase only blind deconvolution for linear phase filters relies on mirror image symmetry in the filter transfer function h z we generalize this deconvolution result to include several other types of symmetries for h z

implementation of 2 d digital filters by iterative methods a two dimensional 2 d rational filter can be implemented by an iterative computation involving only finite extent impulse response fir filtering operations provided a certain convergence criterion is met in this paper we generalize this procedure so that the convergence criterion is satisfied for any stable 2 d rational transfer function one formulation which guarantees convergence invokes a relaxed form of the iterative computation along with prefiltering the numerator and denominator polynomials of the rational transfer function this implementation may be applied with a frequency varying relaxation parameter for increasing the rate of convergence an alternative generalization uses several previously computed iterates unlike our first modification which utilizes only the most recently computed iterate this formulation can potentially guarantee convergence and also increase the convergence rate without the requirement of prefiltering another extension of the iterative computation incorporates constraints e g positivity or finite extent on the output of each iteration proof of convergence of such constrained iterations relies on the concept of a nonexpansive operator in particular the error introduced within the converging solution resulting from a finite extent constraint is shown to satisfy a homogeneous partial difference equation finally this error computation leads to an important link between our iterative implementation with constraints and an iterative solution to partial difference equations e g laplace s equation with known boundary conditions