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)
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