Generalized Schur methods with condition estimators for solving the generalized Sylvester equation

Abstract

Stable algorithms are presented for solving the generalized Sylvester equation. They are based on orthogonal equivalence transformations of the original problem. Perturbation theory and rounding error analysis are included. Condition estimators (dif/sup -1/-estimators) are developed which when substituted into derived error bounds give accuracy estimates of a computed solution. Results from numerical experiments on well-conditioned and ill-conditioned problems are reported.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>