PROJECTION METHODS FOR LARGE-SCALE T-SYLVESTER EQUATIONS

被引:11
作者
Dopico, Froilan M. [1 ]
Gonzalez, Javier [1 ,2 ]
Kressner, Daniel
Simoncini, Valeria [3 ]
机构
[1] Univ Carlos III Madrid, Dept Matemat, Avda Univ 30, Leganes 28911, Spain
[2] Ecole Polytech Fed Lausanne, MATHICSE, ANCHP, Stn 8, CH-1015 Lausanne, Switzerland
[3] Univ Bologna, Dipartimento Matemat, Piazza Porta San Donato 5, I-40127 Bologna, Italy
关键词
Matrix equations; Krylov subspace; iterative methods; large-scale equations; Sylvester equation; Sylvester equation for congruence; ALGEBRAIC RICCATI EQUATION; LYAPUNOV EQUATIONS; NUMERICAL-SOLUTION; MATRIX; AX;
D O I
10.1090/mcom/3081
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:2427 / 2455
页数:29
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