PAD&APPROXIMANTS FOR THE SOLUTION OF A SYTEM OF NONLINEAR EQUATIONS ANNIE Cm-T? and PAUL VAN DER CRUYSSEN University of Antwerp, Department of Mathematics, Universiteitsplein 1, B-2610 Wihijk, Belgium (Receioed January 1981; and in revised form May 1982) Communicated by J. F. Traub Abstract-Let F: R4 *R’ and let x* be a simple root of the system of nonlinear equations F(x) = 0. We will construc...

The identification of instability in large-scale dynamical systems caused by Hopf bifurcation is difficult because of the problem of identifying the rightmost pair of complex eigenvalues of large sparse generalized eigenvalue problems. A new method developed in [Meerbergen and Spence, SIAM J. Matrix Anal. Appl., 31 (2010), pp. 19821999] avoids this computation, instead performing an inverse ite...

this paper presents a comparison between variational iteration method (vim) and modfied variational iteration method (mvim) for approximate solution a system of volterra integral equation of the first kind. we convert a system of volterra integral equations to a system of volterra integro-di®erential equations that use vim and mvim to approximate solution of this system and hence obtain an appr...

The associative memory has been one of the most extensively studied artificial neural networks [1]. The limit storage capacity for the optimal weight matrix is known to be 2N where N is the number of the neurons and the learning algorithm is given by the perceptron learning [2]. The Hebbian rule gives the storage capacity of about 0.14N [3], [4]. The pseudo-inverse type of algorithm yields the ...

A nonlinear Rayleigh-Ritz iterative (NRRIT) method for solving nonlinear eigenvalue problems is studied in this paper. It is an extension of the nonlinear Arnoldi algorithm due to Heinrich Voss. The effienicy of the NRRIT method is demonstrated by comparing with inverse iteration methods to solve a highly nonlinear eigenvalue problem arising from finite element electromagnetic simulation in acc...

We consider the computation of the smallest eigenvalue and associated eigenvector of a Hermitian positive definite pencil. Rayleigh quotient iteration (RQI) is known to converge cubically, and we first analyze how this convergence is affected when the arising linear systems are solved only approximately. We introduce a special measure of the relative error made in the solution of these systems ...

The Jacobi–Davidson method is an eigenvalue solver which uses the iterative (and in general inaccurate) solution of inner linear systems to progress, in an outer iteration, towards a particular solution of the eigenproblem. In this paper we prove a relation between the residual norm of the inner linear system and the residual norm of the eigenvalue problem. We show that the latter may be estima...

A new method for the high-speed computation of double-precision floating-point reciprocal, division, square root, and inverse square root operations is presented in this paper. This method employs a second-degree minimax polynomial approximation to obtain an accurate initial estimate of the reciprocal and the inverse square root values, and then performs a modified Goldschmidt iteration. The hi...

Though the implicitly restarted Arnoldi/Lanczos method in ARPACK is a reliable method for computing a few eigenvalues of large-scale matrices, it can be inefficient because it only checks for convergence at restarts. Significant savings in runtime can be obtained by checking convergence at each Lanczos iteration. We describe a new convergence test for the maximum eigenvalue that is numerically ...

To solve large scale linear equations involved in the Fast Multipole Boundary Element Method (FM-BEM) efficiently, an iterative method named the generalized minimal residual method (GMRES)(m)algorithm with Variable Restart Parameter (VRP-GMRES(m) algorithm) is proposed. By properly changing a variable restart parameter for the GMRES(m) algorithm, the iteration stagnation problem resulting from ...