on the asymptotic stability ofθ methods for delay differential equations stability regions of methods for the linear delay differential test equations begin gathered y t py t qy t tau t 0 hfill y t varphi t t in tau 0 hfill end gathered where is a positive constant are presented in the case thatp andq are real constant coefficients necessary and sufficient conditions on the stepsize for the stability of a method are obtained furthermore whenp andq are complex coefficients sufficient conditions for the stability of the methods are also given

complex elliptically symmetric random variables generation characterization and circularity tests complex elliptically symmetric ces distributions constitute a flexible and broad class of distributions for many engineering applications and include the widely used complex gaussian complex complex generalized gaussian and symmetric stable distributions for example their careful statistical characterization is needed moreover the mechanisms for generating random variables from these distributions are not well defined in literature in this paper we provide such treatment in order to provide a better insight on their statistical properties and simplifying proofs and derivations for example insightful expressions for complex kurtosis coefficients of ces distributions are derived providing an interpretation on what complex kurtosis really measures also derived are asymptotic distributions of circularity measures the sample circularity quotient and coefficient assuming i i d samples from an unspecified ces distribution also new wald s type detectors of circularity are proposed that are valid within ces distributions with finite fourth order moments these results are accompanied with examples that are of interest in developing signal processing algorithms for complex valued signals

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

a class of complex ica algorithms based on the kurtosis cost function in this paper we introduce a novel way of performing real valued optimization in the complex domain this framework enables a direct complex optimization technique when the cost function satisfies the brandwood s independent analyticity condition in particular this technique has been used to derive three algorithms namely kurtosis maximization using gradient update km g kurtosis maximization using fixed point update km f and kurtosis maximization using newton update km n to perform the complex independent component analysis ica based on the maximization of the complex kurtosis cost function the derivation and related analysis of the three algorithms are performed in the complex domain without using any complex real mapping for differentiation and optimization a general complex newton rule is also derived for developing the km n algorithm the real conjugate gradient algorithm is extended to the complex domain similar to the derivation of complex newton rule the simulation results indicate that the fixed point version km f and gradient version km g are superior to other similar algorithms when the sources include both circular and noncircular distributions and the dimension is relatively high

implicit runge kutta nystrom methods for general second order volterra integro differential equations abstract in this paper we derive m stage runge kutta nystrom methods for the numerical solution of general second order volterra integro differential equations these implicit methods are based on collocation techniques in certain polynomial spline spaces the question concerning the attainable order of convergence of such one step methods is completely answered

separation of an instantaneous mixture of gaussian autoregressive sources by the exact maximum likelihood approach this paper deals with the problem of blind separation of an instantaneous mixture of gaussian autoregressive sources without additive noise by the exact maximum likelihood approach the maximization of the likelihood function is divided using relaxation into two suboptimization problems solved by relaxation methods as well the first one consists of the estimation of the separating matrix when the autoregressive structure of the sources is fixed the second one aims at estimating this structure when the separating matrix is fixed we show that the first problem is equivalent to the determinant maximization of the separating matrix under nonlinear constraints we prove the existence and the consistency of the maximum likelihood estimator we also give the expression of fisher s information matrix then we study by computer simulations the performance of our estimator and show the improvement of its achievements w r t both quasimaximum likelihood and second order blind identification sobi estimators

a complex generalized gaussian distribution characterization generation and estimation the generalized gaussian distribution ggd provides a flexible and suitable tool for data modeling and simulation however the characterization of the complex valued ggd in particular generation of samples from a complex ggd have not been well defined in the literature in this correspondence we provide a thorough presentation of the complex valued ggd by i constructing the probability density function pdf ii defining a procedure for generating random numbers from the complex valued ggd and iii implementing a maximum likelihood estimation mle procedure for the shape and covariance parameters in the complex domain we quantify the performance of the mle with simulations and actual radar data

absolute stability of explicit runge kutta nystrom methods for y ƒ x y y abstract we examine absolute stability of s stage explicit runge kutta nystrom r k n methods of order s for s 2 3 4 for y x y y by applying these methods to the test equation y 2 y 2y 0 0 we show the existence of r k n methods of orders two three and four possessing intervals of absolute stability as large as that of explicit runge kutta r k methods of respective orders

nonorthogonal joint diagonalization by combining givens and hyperbolic rotations a new algorithm for computing the nonorthogonal joint diagonalization of a set of matrices is proposed for independent component analysis and blind source separation applications this algorithm is an extension of the jacobi like algorithm first proposed in the joint approximate diagonalization of eigenmatrices jade method for orthogonal joint diagonalization the improvement consists mainly in computing a mixing matrix of determinant one and columns of equal norm instead of an orthogonal mixing matrix this target matrix is constructed iteratively by successive multiplications of not only givens rotations but also hyperbolic rotations and diagonal matrices the algorithm performance evaluated on synthetic data compares favorably with existing methods in terms of speed of convergence and complexity

petrov galerkin methods for linear volterra integro differential equations in this paper we study a class of petrov galerkin solutions that have global optimal convergence rates for linear volterra integro differential equations these solutions also possess certain local and global superconvergence asymptotic expansions of the errors in these solutions are established which can be used to form higher order approximations by richardson extrapolation and defect corrections several postprocessing techniques are introduced to enhance these solutions as by products these higher order numerical approximations can be used to generate a posteriori error estimators representative numerical results are also provided

the multivariate complex normal distribution a generalization the multivariate complex normal distribution usually employed in the literature is a special case since certain restrictions have been imposed on the covariances of the real and imaginary parts of its variables a more general distribution is proposed of which the usual distribution is shown to be a special case

noncircular complex ica by generalized householder reflections we develop an efficient algorithm for noncircular complex independent component analysis ica by optimizing the rows of separation matrix independently using a generalized householder reflector and newton method we apply the new algorithm to the separation of complex generalized gaussian distributed ggd sources and propose a convenient way to learn the noncircularity of the sources simulation results are reported to study the convergence behavior and confirm the superior performance of the new algorithm

nonlinear stability of runge kutta methods for neutral delay integro differential equations the present paper is concerned with the numerical solution to initial value problems of neutral delay integro differential equations ndides the sufficient conditions for the stability and asymptotic stability of runge kutta methods for a class r a b 1 b 2 c of nonlinear systems of ndides are derived a numerical test that confirms the theoretical results is given in the end

solving airline crew scheduling problems by branch and cut the crew scheduling problem is one that has been studied almost continually for the past 40 years but all prior approaches have always approximated the problem of finding an optimal schedule for even the smallest of an airline s fleets the problem is especially important today since costs for flying personnel of major u s carriers have grown and now often exceed 1 3 billion a year and are the second largest item next to fuel cost of the total operating cost of major u s carriers thus even small percentage savings amount to substantial dollar amounts we present a branch and cut approach to solving to proven optimality large set partitioning problems arising within the airline industry we first provide some background related to this important application and then describe the approach for solving representative problems in this problem class the branch and cut solver generates cutting planes based on the underlying structure of the polytope defined by the convex hull of the feasible integer points and incorporates these cuts into a tree search algorithm that uses automatic reformulation procedures heuristics and linear programming technology to assist in the solution numerical experiments are reported for a sample of 68 large scale real world crew scheduling problems these problems include both pure set partitioning problems and set partitioning problems with side constraints these base constraints represent contractual labor requirements and have heretofore not been represented explicitly in the construction of crew schedules thus making it impossible to provide any measure of how far the obtained solution was from optimality an interesting result of obtaining less costly schedules is that the crews themselves are happier with the schedules because they spend more of their duty time flying than waiting on the ground

stability of parallel volterra runge kutta methods abstract in this paper we analyse parallel iteration of volterra runge kutta methods pivrk methods for solving second kind volterra integral equations on parallel computers we focus on the determination of the region of convergence c and on the stability region sm of the iterated method obtained after m iterations results are presented for the convolution test equation it turns out that the stability region sm does not necessarily converge to the stability region s of the corrector however for finite m sm need not to be contained in c or s and may be much larger than c

order conditions for numerical methods for partitioned ordinary differential equations motivated by the consideration of runge kutta formulas for partitioned systems the theory of p series is studied this theory yields the general structure of the order conditions for numerical methods for partitioned systems and in addition for nystrom methods fory f y y for rosenbrock type methods with inexact jacobian w methods it is a direct generalization of the theory of butcher series 7 8 in a later publication the theory ofp series will be used for the derivation of order conditions for runge kutta type methods for volterra integral equations 1

unconditionally stable difference methods for delay partial differential equations this paper is concerned with the numerical solution of parabolic partial differential equations with time delay we focus in particular on the delay dependent stability analysis of difference methods that use a non constrained mesh i e the time step size is not required to be a submultiple of the delay we prove that the fully discrete system unconditionally preserves the delay dependent asymptotic stability of the linear test problem under consideration when the following discretization is used a variant of the classical second order central differences to approximate the diffusion operator a linear interpolation to approximate the delay argument and finally the trapezoidal rule or the second order backward differentiation formula to discretize the time derivative we end the paper with some numerical experiments that confirm the theoretical results

implicit runge kutta methods of optimal order for volterra integro differential equations implicit runge kutta methods with m stages and optimal order p 2m for the approximate solution of volterra integro differential equations can be viewed as fully dis cretized collocation methods in certain polynomial spline spaces the choice of the quadrature formulas needed for the full discretization of the collocations is investigated and it is shown that in contrast to ordinary differential equations there exist for fixed m several optimal methods 1 introduction in this paper we shall be concerned with the approximate solution of the initial value problem for a nonlinear first order volterra integro differential equation

runge kutta theory for volterra integrodifferential equations the present paper develops the theory of general runge kutta methods for volterra integrodifferential equations the local order is characterized in terms of the coefficients of the method we investigate the global convergence of mixed and extended runge kutta methods and give results on asymptotic error expansions in a further section we construct examples of methods up to order 4

on the t method for delay differential equations with infinite lag abstract this paper discusses the method for the numerical solution of delay differential equations with infinite lag our analysis is based on the test equation y t ay t by t where a b c and 0 1 in order to solve the storage problem involved in studying the long time behaviour of the solution we use a grid with increased stepsizes monotonicity uniform boundedness asymptotic stability algebraic decay and global discretisation error of the numerical solution are investigated

the further study of a certain nonlinear integro differential equation in this paper the writers give a global existence and uniqueness theorem for a nonlinear integro differential equation which occurs in the statistical theory of turbulent diffusion the theorem is more general than that presented by s h chang and j t day j comput phys 26 1978 162 the problems of the existence and uniqueness of a solution to the equation are solved completely implicit runge kutta methods with m stages and optimal order p 2m for the approximate solution of the equation are introduced computational examples are also considered

nonorthogonal joint diagonalization free of degenerate solution the problem of approximate joint diagonalization of a set of matrices is instrumental in numerous statistical signal processing applications for nonorthogonal joint diagonalization based on the weighted least squares wls criterion the trivial zero solution can simply be avoided by adopting some constraint on the diagonalizing matrix or penalty terms however the resultant algorithms may converge to some undesired degenerate solutions nonzero but singular or ill conditioned solutions this paper discusses and analyzes the problem of degenerate solutions in detail to solve this problem a novel nonleast squares criterion for approximate nonorthogonal joint diagonalization is proposed and an efficient algorithm called fast approximate joint diagonalization fajd is developed as compared with the existing nonorthogonal diagonalization algorithms the new algorithm can not only avoid the trivial solution but also any degenerate solutions theoretical analysis shows that the fajd algorithm has some advantages over the existing nonorthogonal diagonalization algorithms simulation results are presented to demonstrate the efficiency of this paper s algorithm

on extending the complex fastica algorithm to noncircular sources the complex fast independent component analysis c fastica algorithm is one of the most ubiquitous methods for solving the ica problems with complex valued data in this study we extend the work of bingham and hyvarinen to the more general case of noncircular sources by deriving a new fixed point algorithm that uses the information in the pseudo covariance matrix this modification provides significant improvement in performance when confronted with noncircular sources specifically with sub gaussian noncircular signals such as binary phase shift keying bpsk signals where c fastica fails to achieve separation we also present a rigorous local stability analysis that we use to quantify the effects of noncircularity on performance simulations are presented to demonstrate the effectiveness of our method

runge kutta theory for volterra integral equations of the second kind the present paper develops the theory of general runge kutta methods for volterra integral equations of the second kind the order conditions are derived by using the theory of p series which for our problem reduces to the theory of v series these results are then applied to two special classes of runge kutta methods introduced by pouzet and by bel tyukov

second order statistics of complex signals the second order statistical properties of complex signals are usually characterized by the covariance function however this is not sufficient for a complete second order description and it is necessary to introduce another moment called the relation function its properties and especially the conditions that it must satisfy are analyzed both for stationary and nonstationary signals this leads to a new perspective concerning the concept of complex white noise as well as the modeling of any signal as the output of a linear system driven by a white noise finally this is applied to complex autoregressive signals and it is shown that the classical prediction problem must be reformulated when the relation function is taken into consideration

complex ica using nonlinear functions we introduce a framework based on wirtinger calculus for nonlinear complex valued signal processing such that all computations can be directly carried out in the complex domain the two main approaches for performing independent component analysis maximum likelihood and maximization of non gaussianity which are intimately related to each other are studied using this framework the main update rules for the two approaches are derived their properties and density matching strategies are discussed along with numerical examples to highlight their relationships

discrete time waveform relaxation volterra runge kutta methods convergence analysis the discrete time relaxation methods based on volterra runge kutta methods for solving large system of second kind volterra integral equations are proposed convergence of the discrete time iteration process with particular attention to parallel methods is investigated

natural continuous extensions of runge kutta methods the present paper develops a theory of natural continuous extensions nces for the discrete approximate solution of an ode given by a runge kutta process these nces are defined in such a way that the continuous solutions furnished by the one step collocation methods are included

high order methods for the numerical solution of volterra integro differential equations abstract if a first order volterra integro differential equation is solved by collocation in the space of continuous polynomial splines of degree m 1 with collocation occuring at the gauss legendre points then the resulting approximation u converges at its knots like o h 2m while its derivative u exhibits only o h m convergence this paper deals with the question of how to choose the collocation points so that both u and u converge like o h q with q maximal

on the stability of runge kutta methods for delay integral equations we present a class of runge kutta methods for the numerical solution of a class of delay integral equations dies described by two different kernels and with a fixed delay the stability properties of these methods are investigated with respect to a test equation with linear kernels depending on complex parameters the results are then applied to collocation methods in particular we obtain that any collocation method for dies resulting from ana stable collocation method for odes with a stepsize which is submultiple of the delay preserves the asymptotic stability properties of the analytic solutions

stability of runge kutta methods for delay integro differential equations we study stability of runge kutta rk methods for delay integro differential equations with a constant delay on the basis of the linear equation du dt lu t mu t k t t u d where l m k are constant complex matrices in particular we show that the same result as in the case k 0 koto bit 34 1994 262 267 holds for this test equation i e every a stable rk method preserves the delay independent stability of the exact solution whenever a step size of the form h m is used where m is a positive integer

convergence results for continuous time waveform methods for volterra integral equations in this paper the waveform methods for solving systems of second kind volterra integral equations are introduced the convergence properties of continuous time waveform methods on finite length and infinite length time intervals are investigated with particular regard to parallel waveform relaxation methods

collocation methods for nonlinear volterra integro differential equations with infinite delay in this paper we study the numerical solution of nonlinear volterra integrodifferential equations with infinite delay by spline collocation and related runge kutta type methods the kernel function in these equations is of the form k t 8 y t y s with a representative example given by volterra s population equation where we have k t a y t y 8 a t s g y t y 8

blind separation of noncircular correlated sources using gaussian entropy rate we introduce a new blind source separation bss algorithm for correlated noncircular sources that uses only second order statistics and fully takes the correlation structure into account we propose a parametric entropy rate estimator that uses a widely linear autoregressive ar model for the sources and derive the bss algorithm by minimizing the mutual information of separated time series we compare the performance of the new algorithm with competing algorithms and demonstrate its superior separation performance as well as its effectiveness in separation of non gaussian sources when the identification conditions are met

spline collocation methods for nonlinear volterra integral equations with unknown delay in this paper we introduce and study polynomial spline collocation methods for systems of volterra integral equations with unknown lower integral limit arising in mathematical economics their discretization leads to implicit runge kutta type methods the global convergence and local superconvergence properties of these methods are proved and the theory is illustrated by a numerical example arising in the application of such equations in certain mathematical models of liquidation

stability analysis of numerical methods for linear neutral volterra delay integro differential system this paper is concerned with the stability of numerical methods for linear neutral volterra delay integro differential system a sufficient condition such that the system is asymptotically stable is derived furthermore it is proved that every linear q method with email protected 1 2 1 and a stable bdf method preserve the delay independent stability of its exact solutions finally the numerical experiments are given to demonstrate the conclusions

natural continuous extensions of runge kutta methods for volterra integral equations of the second kind and their applications we consider a very general class of runge kutta methods for the numerical solution of volterra integral equations of the second kind which includes as special cases all the more important methods which have been considered in the literature the main purpose of this paper is to define and prove the existence of the natural continuous extensions nce s of runge kutta methods i e piecewise polynomial functions which extend the approximation at the grid points to the whole interval of integration the particular properties required of the nce s allow us to construct the tail approximations which are quite efficient in terms of kernel evaluations

joint blind source separation with multivariate gaussian model algorithms and performance analysis in this paper we consider the joint blind source separation jbss problem and introduce a number of algorithms to solve the jbss problem using the independent vector analysis iva framework source separation of multiple datasets simultaneously is possible when the sources within each and every dataset are independent of one another and each source is dependent on at most one source within each of the other datasets in addition to source separation the iva framework solves an essential problem of jbss namely the identification of the dependent sources across the datasets we propose to use the multivariate gaussian source prior to achieve jbss of sources that are linearly dependent across datasets analysis within the paper yields the local stability conditions nonidentifiability conditions and induced cramer rao lower bound on the achievable interference to source ratio for iva with multivariate gaussian source priors additionally by exploiting a novel nonorthogonal decoupling of the iva cost function we introduce both newton and quasi newton optimization algorithms for the general iva framework

polynomial spline collocation methods for the nonlinear basset equation abstract we discuss the application of a class of spline collocation methods to a first order volterra integro differential equation arising in fluid dynamics since this equation possesses a weakly singular kernel its solutions even for analytic data are not smooth on the entire interval of integration it is shown that while the use of uniform grids leads to poor convergence rates high order convergence is restored on suitably graded grids

super exponential methods for blind deconvolution a class of iterative methods for solving the blind deconvolution problem i e for recovering the input of an unknown possibly nonminimum phase linear system by observation of its output is presented these methods are universal do not require prior knowledge of the input distribution are computationally efficient and statistically stable and converge to the desired solution regardless of initialization at a very fast rate the effects of finite length of the data finite length of the equalizer and additive noise in the system on the attainable performance intersymbol interference are analyzed it is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems recursive and sequential algorithms are also developed which allow real time implementation and adaptive equalization of time varying systems

stability analysis of theta methods for neutral functional differential equations this paper deals with the subject of numerical stability for the neutral functional differential equation y t ay t by qt cy pt qquad t 0 it is proved that numerical solutions generated by theta methods are convergent if c b if and only if theta geq 1 2 and that the one leg theta method is lambda stable if theta 1 we also find out that inappropriate stepsize causes spurious solution in the marginal case where rm re a 0 and a b

on entropy rate for the complex domain and its application to i i d sampling we derive the entropy rate formula for a complex gaussian random process by using a widely linear model the resulting expression is general and applicable to both circular and noncircular gaussian processes since any second order stationary process can be modeled as the output of a widely linear system driven by a circular white noise furthermore we demonstrate application of the derived formula to an order selection problem we extend a scheme for independent and identically distributed i i d sampling to the complex domain to improve the estimation performance of information theoretic criteria when samples are correlated we show the effectiveness of the approach for order selection for simulated and actual functional magnetic resonance imaging fmri data that are inherently complex valued

stability of linear multistep methods for delay integro differential equations this paper is concerned with the numerical solution of delay integro differential equations the adaptation of linear multistep methods is considered the emphasis is on the linear stability of numerical methods it is shown that every a stable strongly 0 stable linear multistep method of pouzet type can preserve the delay independent stability of the underlying linear systems in addition some delay dependent stability conditions for the stability of numerical methods are also given

dissipativity of linear θ methods for integro differential equations this paper is concerned with the analytic and numerical dissipativity of nonlinear integro differential equations ides a dissipativity criteria for ides is given it is shown that any a stable linear 0 method for the systems is dissipative numerical examples are given to confirm the theoretical results

noncircular principal component analysis and its application to model selection one of the most commonly used data analysis tools principal component analysis pca since is based on variance maximization assumes a circular model and hence cannot account for the potential noncircularity of complex data in this paper we introduce noncircular pca ncpca which extends the traditional pca to the case where there can be both circular and noncircular gaussian signals in the subspace we study the properties of ncpca introduce an efficient algorithm for its computation and demonstrate its application to model selection i e the detection of both the signal subspace order and the number of circular and noncircular signals we present numerical results to demonstrate the advantages of ncpca over regular pca when there are noncircular signals in the subspace at the same time we note that since a noncircular model has more degrees of freedom than a circular one there are cases where a circular model might be preferred even though the underlying problem is noncircular in particular we show that a circular model is preferred when the signal to noise ratio snr is low number of samples is small or the degree of noncircularity of the signals is low hence ncpca inherently provides guidance as to when to take noncircularity into account

stability analysis of the de hoog and weiss implicit runge kutta methods for the volterra integral and integrodifferential equations abstract the stability of the de hoog and weiss runge kutta methods is analyzed for the volterra integrodifferential equations with respect to the basic test equation and for volterra integral equations with respect to the linear convolution equation stability regions are determined for some choices of the parameters

piecewise polynomial collocation methods for linear volterra integro differential equations with weakly singular kernels in the first part of this paper we study the regularity properties of solutions of linear volterra integro differential equations with weakly singular or other nonsmooth kernels we then use these results in the analysis of two piecewise polynomial collocation methods for solving such equations numerically the main purpose of the paper is the derivation of optimal global convergence estimates and the analysis of the attainable order of local superconvergence at the collocation points

the stability of difference formulas for delay differential equations a new simple geometric technique is presented for analyzing the stability of difference formulas for the model delay differential equation y t py t qy t 8 where p and q are complex constants and the delay 8 is a positive constant the technique is based on the argument principle and directly relates the region of absolute stability for ordinary differential equations corresponding to the py t term with the region corresponding to the delay term qy t 8 a sufficient condition for stability is that these regions be disjoint the technique is used to show that for each a stable a a stable or stiffly stable linear multistep formula for ordinary differential equations there is a correspond ing linear multistep formula for delay differential equations with analogous stability properties the analogy does not extend however to a stable one step formulas

numerical stability of the t methods for systems of differential equations with several delay terms abstract consider the following two dimensional delay differential equation dde u t a 1 u t b 1 v t d 2 v t a 2 v t b 2 u t d 1 t t 0 with the initial conditions u t u 0 t t 0 d 1 t t 0 v t v 0 t t 0 d 2 t t 0 where a j b j c d j 0 and u 0 t 0 t are continuous and complex valued the author give the sufficient conditions for the asymptotic stability of equation 0 1 the numerical stabilities of the linear method and the one leg method are investigated by analysing their stabilities behaviour in the solutions of 0 1 it is shown that the linear method is gp stable if and only if 1 2 1 and that the one leg method is gp stable if and only if 1

a repeated matching heuristic for the single source capacitated facility location problem facility location models form an important class of integer programming problems with application in many areas such as the distribution and transportation industries an important class of solution methods for these problems are so called lagrangean heuristics which have been shown to produce high quality solutions and which are at the same time robust the general facility location problem can be divided into a number of special problems depending on the properties assumed in the capacitated location problem each facility has a specific capacity on the service it provides we describe a new solution approach for the capacitated facility location problem when each customer is served by a single facility the approach is based on a repeated matching algorithm which essentially solves a series of matching problems until certain convergence criteria are satisfied the method generates feasible solutions in each iteration in contrast to lagrangean heuristics where problem dependent heuristics must be used to construct a feasible solution numerical results show that the approach produces solutions which are of similar and often better than those produced using the best lagrangean heuristics

highly stable parallel volterra runge kutta methods a new family of parallel v stable methods for second kind volterra integral equations are proposed the methods belong to the class of volterra runge kutta methods and can be applied provided that some not very restrictive conditions on the integral equation kernel are satisfied

parallel algorithm with spectral convergence for nonlinear integro differential equations we discuss a numerical algorithm for solving nonlinear integro differential equations and illustrate our findings for the particular case of volterra type equations the algorithm combines a perturbation approach meant to render a linearized version of the problem and a spectral method where unknown functions are expanded in terms of chebyshev polynomials el gendi s method this approach is shown to be suitable for the calculation of two point green functions required in next to leading order studies of time dependent quantum field theory

stability of θ methods for delay integro differential equations stability of methods for delay integro differential equations dides is studied on the basis of the linear equation du dt u t u t k t t u d where k are complex numbers and is a constant delay it is shown that every a stable method possesses a similar stability property to p stability i e the method preserves the delay independent stability of the exact solution under the condition that k is real and h is an integer where h is a step size it is also shown that the method does not possess the same property if h is not an integer as a result no method can possess a similar stability property to gp stability with respect to dides

applications and numerical analysis of partial differential volterra equations a brief survey this article contains a concise survey of the numerical analysis of volterra equations and leads up to some recent results on a posteriori error estimation for finite element approximations

blind separation of mixture of independent sources through a quasi maximum likelihood approach we propose two methods for separating mixture of independent sources without any precise knowledge of their probability distribution they are obtained by considering a maximum likelihood ml solution corresponding to some given distributions of the sources and relaxing this assumption afterward the first method is specially adapted to temporally independent non gaussian sources and is based on the use of nonlinear separating functions the second method is specially adapted to correlated sources with distinct spectra and is based on the use of linear separating filters a theoretical analysis of the performance of the methods has been made a simple procedure for optimally choosing the separating functions is proposed further in the second method a simple implementation based on the simultaneous diagonalization of two symmetric matrices is provided finally some numerical and simulation results are given illustrating the performance of the method and the good agreement between the experiments and the theory

natural continuous extensions of runge kutta methods for volterra integrodifferential equations in this paper we deal with a very general class of runge kutta methods for the numerical solution of volterra integrodifferential equations our main contribution is the development of the theory of natural continuous extensions nces i e piecewice polynomial functions which interpolate the values given by the rk method at the mesh points the particular features of these nces allow us to construct tail approximations which are quite efficient since they require a minimal number of kernel evaluations

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

on the integer properties of scheduling set partitioning models abstract many scheduling problems arising in the transportation industry can be posed as massive set partitioning zero one integer programmes for reasons of computational complexity it is generally unrealistic to attempt to solve the model in this form using conventional integer linear programming by the imposition of additional structure derived from the real world problem but not already implicit in the mathematical model it is possible to significantly reduce the effects of computational complexity and provide an effective method of obtaining good feasible solutions in this paper recent results in graph theory concerning natural integer properties of set partitioning integer programmes are discussed these results motivate the development of further implicit constraints which simultaneously reduce the dimensionality and increase the proportion of integer basic feasible solutions of the set partitioning linear programme

an h p version of the continuous petrov galerkin finite element method for volterra integro differential equations with smooth and nonsmooth kernels we present an h p version of the continuous petrov galerkin cpg finite element method for linear volterra integro differential equations with smooth and nonsmooth kernels we establish a priori error estimates in the l 2 h 1 and l infty norms that are completely explicit with respect to the local discretization and regularity parameters for singular solutions caused by the weakly singular kernels we prove that algebraic convergence rates can be achieved for the h p version of the cpg method with quasi uniform meshes moreover we show that exponential rates of convergence can be achieved for solutions with start up singularities by using geometric time partitions and linearly increasing polynomial degrees numerical experiments are provided to illustrate the theoretical results

equivariant adaptive source separation source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed this paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence easi the easi algorithms are based on the idea of serial updating this specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures most importantly the performance of an easi algorithm does not depend on the mixing matrix in particular convergence rates stability conditions and interference rejection levels depend only on the normalized distributions of the source signals closed form expressions of these quantities are given via an asymptotic performance analysis the theme of equivariance is stressed throughout the paper the source separation problem has an underlying multiplicative structure the parameter space forms a matrix multiplicative group we explore the favorable consequences of this fact on implementation performance and optimization of easi algorithms

on circularity circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors however this concept can be extended in various ways for nonnormal vectors the first purpose of the paper is to introduce and compare some possible definitions of circularity from these definitions it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components therefore the relationships between circularity and stationarity are analyzed in detail finally the theory of linear mean square estimation for complex signals exhibits some connections with circularity and it is shown that without this assumption the estimation theory must be reformulated

an exact algorithm for the capacitated facility location problems with single sourcing facility location problems are often encountered in many areas such as distribution transportation and telecommunication we describe a new solution approach for the capacitated facility location problem in which each customer is served by a single facility an important class of heuristic solution methods for these problems are lagrangian heuristics which have been shown to produce high quality solutions and at the same time be quite robust a primal heuristic based on a repeated matching algorithm which essentially solves a series of matching problems until certain convergence criteria are satisfied is incorporated into the lagrangian heuristic finally a branch and bound method based on the lagrangian heuristic is developed and compared computationally to the commercial code cplex the computational results indicate that the proposed method is very efficient

a spectral collocation method for multidimensional nonlinear weakly singular volterra integral equation abstract this paper is concerned with the convergence properties of chebyshev spectral collocation method when used to approximate the solution of multidimensional nonlinear volterra integral equation of the second kind with a weakly singular kernel we consider the case that the underlying solution is sufficiently smooth the chebyshev collocation discretization is proposed for this equation in the present paper we provide a rigorous error analysis which justifies that the errors of approximate solution decay exponentially in weighted l 2 norm and l norm numerical results are presented to demonstrate the effectiveness of the spectral method

weak delay dependent stability of runge kutta methods for differential systems with distributed delays abstract this paper discusses the stability of runge kutta methods for differential systems with distributed delays weak delay dependent stability of pouzet type runge kutta methods is studied in this paper it is revealed that under suitable conditions runge kutta methods preserve weak delay dependent stability an algorithm is employed to check weak delay dependent stability of numerical solutions and the effectiveness of the derived theoretical results is demonstrated with numerical examples

nonorthogonal joint diagonalization algorithm based on trigonometric parameterization the joint diagonalization technique is an important type of method for blind source separation in this paper a new approach is presented to joint diagonalization for a set of symmetric matrices with a general and not necessarily orthogonal matrix the approach performs joint diagonalization via a series of symmetric eigen decompositions including merits of simplicity effectiveness and computational efficiency simulation results demonstrate the potential improvement of the performance in the context of blind source separation

an efficient algorithm for solving volterra integro differential equations based on alpert s multi wavelets galerkin method abstract this paper is concerned with the application of the multi wavelets galerkin method to linear and nonlinear second order volterra integro differential equations using the operational matrices of integration and wavelet transform matrix we reduce the problem to a set of algebraic equations for linear type we use thresholding to reduce the computational effort we demonstrate that our solutions may be efficiently represented in a multi wavelets basis due to flexible vanishing moments property of this type of multi wavelets the l 2 convergence of the scheme for the proposed equation has been investigated a series of numerical tests is provided to demonstrate the validity and applicability of the technique

aircrew schedule generation using repeated matching we consider the aircrew scheduling problem of determining tours of duty tods for aircrews given a set of sectors or flights requiring regular crews a regular crew consists of two crew members but by including supplementary crew a third pilot on some sectors it is possible to extend duty periods to generate more cost efficient tods a related problem is thus to generate tods for these third pilots but the sectors requiring a third pilot are not known in advance to solve these two related problems simultaneously we apply a heuristic procedure that solves a sequence of matching problems i e a repeated matching algorithm numerical results based on the solution of a real problem show that this approach is a valid and efficient method for solving the aircrew scheduling problem especially when there is the option of using supplementary crew to extend duty periods

p stability properties of runge kutta methods for delay differential equations recently the author and others have studied a class of runge kutta methods for ddes these methods make use of certain constrained meshes which allow to get optimal order results in this paper we study their asymptotic stability properties using the test equation begin gathered y t ay t by t tau t 0 hfill y t g t for tau leqq t leqq 0 hfill end gathered wherea b 0 andg t is continuous and complex valued it is known thaty t 0 ast if b re a in particular we show that any astable one step collocation method for odes inherits the same property when it is applied to ddes with a constrained mesh i e it is p stable

a coordinate descent algorithm for complex joint diagonalization under hermitian and transpose congruences abstract this paper deals with the problem of joint complexmatrix diagonalization by considering both the hermitian andtranspose congruences we address the general case where thesearched diagonalizing matrix is apriori nonunitary based onthe minimization of a quadratic criterion we propose a ex ible algorithm in the sense that it allows to directly consider arectangular diagonalizing matrix and to take into considerationboth the hermitian and transpose congruences within the sameframework the proposed algorithm is a coordinate descentalgorithm that is based on an approximate criterion leading to theanalytical derivation of the minima arguments computer simu lations are drawn to illustrate the usefulness and performancesof the algorithm and a comparison to state of the art algorithmsis presented finally an application to independent componentanalysis based on fourth order statistics is also presented index terms blind source separation complex symmetric ma trices hermitian matrices independent component analysis jointdiagonalization

stability properties of interpolants for runge kutta methods in solving initial value problems for ordinary differential equations by means of a discrete method we often need to know the solution on a set of points that differs from the grid systems with driving equation dense output discontinuity problems delay equations etc the nonnodal approximations are generally obtained by local interpolation and different features can be requested from the interpolants according to the problem treated in this paper we introduce the concept of stable interpolant for runge kutta methods roughly speaking a stable interpolant maintains the stability properties of the runge kutta method itself the lack of such stability makes the continuous extension not reliable especially in solving stiff equations

complex random vectors and ica models identifiability uniqueness and separability in this paper the conditions for identifiability separability and uniqueness of linear complex valued independent component analysis ica models are established these results extend the well known conditions for solving real valued ica problems to complex valued models relevant properties of complex random vectors are described in order to extend the darmois skitovich theorem for complex valued models this theorem is used to construct a proof of a theorem for each of the above ica model concepts both circular and noncircular complex random vectors are covered examples clarifying the above concepts are presented

asymptotic stability analysis of θ methods for functional differential equations stability analysis of methods for functional differential equations based on the test equation begin gathered y t ay t lambda by t t 0 hfill y t psi t t in left lambda 0 right hfill end gathered 0 is presented it is known thaty t 0 ast if and only if b a and we investigate whether this property is inherited by the numerical solution approximatingy

dissipativity of θ methods for nonlinear volterra delay integro differential equations this paper deals with the analytic and numerical dissipativity of nonlinear volterra delay integro differential equations vdides a dissipativity criteria for vdides is given we investigate the dissipativity properties of one leg q methods and linear q methods for the underlying systems it is shown that for q 12 1 any one leg q method and linear q method can inherit the dissipativity of the underlying systems

the numerical analysis of implicit runge kutta methods for a certain nonlinear integro differential equation the mathematical theory and numerical methods for the nonlinear integro differential equation u t p t u t 0 t k t s u t s u s ds q t 0 t t u 0 u 0 it is proved that the implicit runge kutta methods with m stages are of optimal approximation order p 2m

non orthogonal joint diagonalization in the least squares sense with application in blind source separation approximate joint diagonalization of a set of matrices is an essential tool in many blind source separation bss algorithms a common measure of the attained diagonalization of the set is the weighted least squares wls criterion however most well known algorithms are restricted to finding an orthogonal diagonalizing matrix relying on a whitening phase for the nonorthogonal factor often such an approach implies unbalanced weighting which can result in degraded performance we propose an iterative alternating directions algorithm for minimizing the wls criterion with respect to a general not necessarily orthogonal diagonalizing matrix under some mild assumptions we prove weak convergence in the sense that the norm of parameters update is guaranteed to fall below any arbitrarily small threshold within a finite number of iterations we distinguish between hermitian and symmetrical problems using bss simulations results we demonstrate the improvement in estimating the mixing matrix resulting from the relaxation of the orthogonality restriction

retarded differential equations retarded differential equations rdes are differential equations having retarded arguments they arise in many realistic models of problems in science engineering and medicine where there is a time lag or after effect numerical techniques for such problems may be regarded as extensions of dense output methods for ordinary differential equations odes but scalar rdes are inherently infinite dimensional with a richer structure than their ode counterparts we give background material develop a theoretical foundation for the basic numerics and give some results not previously published