Projection methods for large-scale T-Sylvester equations Articles uri icon

publication date

  • September 2016

start page

  • 2427

end page

  • 2455

issue

  • 1

volume

  • 85

international standard serial number (ISSN)

  • 0025-5718

electronic international standard serial number (EISSN)

  • 1088-6842

abstract

  • 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 e cient 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 di erent 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, o ering a 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; algebraic riccati equation; krylov subspace methods; lyapunov equations; descriptor systems; invariant subspaces; numerical solution; low rank; ax; xa