Projection Methods For Large-Scale T-Sylvester Equations

• Published in: Mathematics Of Computation (ISSN: 0025-5718), vol. 85, num. 1, p. 2427-2455
• Providence: Amer Mathematical Soc, 2016

The matrix Sylvester equation for congruence, or T-Sylvester equation, has recently attracted considerable attention as a consequence of its close relation to palindromic eigenvalue problems. The theory concerning T-Sylvester equations is rather well understood, and there are stable and efficient numerical algorithms which solve these equations for small- to medium-sized matrices. However, developing numerical algorithms for solving large-scale T-Sylvester equations still remains an open problem. In this paper, we present several projection algorithms based on different Krylov spaces for solving this problem when the right-hand side of the T-Sylvester equation is a low-rank matrix. The new algorithms have been extensively tested, and the reported numerical results show that they work very well in practice, offering clear guidance on which algorithm is the most convenient in each situation.

Keywords: Matrix equations ; Krylov subspace ; iterative methods ; large-scale equations ; Sylvester equation ; Sylvester equation for congruence

Reference

• EPFL-ARTICLE-222176
• doi:10.1090/mcom/3081
• View record in Web of Science

Record created on 2016-10-18, modified on 2017-05-12