Rounding error and perturbation bounds for the symplectic QR factorization

摘要

To compute the eigenvalues of a skew-symmetric matrix A, we can use a one-sided Jacobi-like algorithm to enhance accuracy. This algorithm begins by a suitable. Cholesky-like factorization of A, A = G(T)JG. In some applications, A is given implicitly in that form and its natural Cholesky-like factor G is immediately available, but "tall", i.e., not of full row rank. This factor G is unsuitable for the Jacobi-like process. To avoid explicit computation of A, and possible loss of accuracy, the factor has to be preprocessed by a QR-like factorization. In this paper we present the symplectic QR algorithm to achieve such a factorization, together with the corresponding rounding error and perturbation bounds. These bounds fit well into the relative perturbation theory for skew-symmetric matrices given in factorized form. (C) 2002 Elsevier Science Inc. All rights reserved. [References: 10]