Projection Methods For Large-Scale T-Sylvester Equations

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.


Published in:
Mathematics Of Computation, 85, 1, 2427-2455
Year:
2016
Publisher:
Providence, Amer Mathematical Soc
ISSN:
0025-5718
Keywords:
Laboratories:




 Record created 2016-10-18, last modified 2018-03-17


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