Accession Number : AD0787237

Title :   Perturbation Bounds for the QR Factorization of a Matrix. Technical rept.,

Corporate Author : MARYLAND UNIV COLLEGE PARK COMPUTER SCIENCE CENTER

Personal Author(s) : Stewart,G. W.

Report Date : SEP 1974

Pagination or Media Count : 23

Abstract : Let A be an m x n matrix of rank n. The QR factorization of A decomposes A into the product of an m x n matrix Q with orthonormal columns and a nonsingular upper triangular matrix R. The decomposition is essentially unique, Q being determined up to the signs of its columns and R up to the signs of its rows. If E is an m x n matrix such that A + E is of rank n, then A + E has an essentially unique factorization (Q+W) (R+F). In this paper bounds on //W// and //F// in terms of //E// are given. In addition perturbation bounds are given for the closely related Cholesky factorization of a positive definite matrix B into the product (R sup T) of a lower triangular matrix and its transpose. (Author)

Descriptors :   *Matrices(Mathematics), Perturbations, Inequalities, Theorems

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE