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This paper is concerned with the problem of blind separation of an instantaneous mixture of sources (BSS), which has been addressed in many ways. When power spectral densities of the sources are different, methods using second-order statistics are sufficient to solve this problem. Otherwise, these methods fail and others (higher order statistics, etc.) must be used. In this paper, we propose an iterative method to process the case of sources with the same power spectral density. This method is based on an evaluation of conditional first and second-order statistics only. Restrictions on characteristics of sources are given to reach a solution, and proofs of convergence of the algorithm are provided for particular cases of probability density functions. Robustness of this algorithm with respect to the number of sources is shown through computer simulations. A particular case of sources that have a probability density function with unbounded domain of definition is described; here, the algorithm does not lead directly to a separation state but to an a priori known mixture state. Finally, prospects of links with contrast functions are mentioned, with a possible generalization of them based on results obtained with particular sources. [ABSTRACT FROM AUTHOR]

Solving large sparse linear systems is essential in numerous scientific domains. Several algorithms, based on direct or iterative methods, have been developed for parallel architectures. On distributed grids consisting of processors located in distant geographical sites, their performance may be unsatisfactory because they suffer from too many synchronizations and communications. The GREMLINS code has been developed for solving large sparse linear systems on distributed grids. It implements the multisplitting method that consists in splitting the original linear system into several subsystems that can be solved independently. In this paper, the performance of the GREMLINS code obtained with several libraries for solving the linear subsystems is analyzed. Its performance is also compared with that of the widely used PETSc library that enables one to develop portable parallel applications. Numerical experiments have been carried out both on local clusters and on distributed grids. [ABSTRACT FROM AUTHOR]

Abstract: A nonlinear iteration method for solving a class of two-dimensional nonlinear coupled systems of parabolic and hyperbolic equations is studied. A simple iterative finite difference scheme is designed; the calculation complexity is reduced by decoupling the nonlinear system, and the precision is assured by timely evaluation updating. A strict theoretical analysis is carried out as regards the convergence and approximation properties of the iterative scheme, and the related stability and approximation properties of the nonlinear fully implicit finite difference (FIFD) scheme. The iterative algorithm has a linear constringent ratio; its solution gives a second-order spatial approximation and first-order temporal approximation to the real solution. The corresponding nonlinear FIFD scheme is stable and gives the same order of approximation. Numerical tests verify the results of the theoretical analysis. The discrete functional analysis and inductive hypothesis reasoning techniques used in this paper are helpful for overcoming difficulties arising from the nonlinearity and coupling and lead to a related theoretical analysis for nonlinear FI schemes. [Copyright &y& Elsevier]

Abstract: This paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of boundary value problems in the reproducing kernel space. The analytical solution and approximate solution are represented in terms of series. For any initial function , we prove , , . Two numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective. [Copyright &y& Elsevier]

An iterative method is proposed to solve the Schrödinger eigenvalue problem in a wavelet framework. Orthonormal wavelets are used to represent the corresponding operator as a sparse band matrix. This representation, called the nonstandard (NS) form, is obtained by means of the Beylkin­Coifman­Rokhlin (BCR) algorithm and simplifies the numerical calculations. Problems due to the one-dimensional mathematical model and to the discretization process receive special attention. [ABSTRACT FROM AUTHOR]