Perturbation Bounds for the QR Factorization of a Matrix. Technical rept.,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1974
- Accession Number
- AD0787237
Entities
People
- Gilbert W. Stewart
Organizations
- University of Maryland