
Accession Number : AD0765748
Title : The Convergence of the Method of Conjugate Gradients at Isolated Extreme Points of the Spectrum,
Corporate Author : CARNEGIEMELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE
Personal Author(s) : Stewart,G. W.
Report Date : AUG 1973
Pagination or Media Count : 19
Abstract : Let A be a positive definite matrix with a simple eigenvalue (lambda sub 1) that lies outside an interval (alpha,beta) containing the remaining eigenvalues. Let the method of conjugate gradients be applied to the solution of the linear system Az = b producing a sequence of iterates z sub 0,z sub 1,... and an associated sequence of error vectors (e sub i) = z  (z sub i). In the paper bounds are obtained for the component of the error vector lying along the eigenvector associated with (lambda sub 1). The bounds imply that, provided (lambda sub 1) is well separated from (alpha,beta), this component will decrease rapidly even when the matrix A is moderately ill conditioned. (Author)
Descriptors : (*MATRICES(MATHEMATICS), APPROXIMATION(MATHEMATICS)), POLYNOMIALS, CONVERGENCE
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE