摘要
Abstract In this paper, we investigate the effective condition numbers for the generalized Sylvester equation （AX - YB, DX - YE） = （C,F）, where A,D ∈ Rm×m B,E ∈ Rn×n and C,F ∈ Rm×n. We apply the small sample statistical method for the fast condition estimation of the generalized Sylvester equation, which requires （9（m2n ＋ mn2） flops, comparing with （-O（m3 ＋ n3） flops for the generalized Schur and generalized Hessenberg- Schur methods for solving the generalized Sylvester equation. Numerical examples illustrate the sharpness of our perturbation bounds.
In this paper,we investigate the effective condition numbers for the generalized Sylvester equation(AX-YB,DX-YE)=(C,F),where A,D∈R m×m,B,E∈R n×n and C,F ∈ R m×n.We apply the small sample statistical method for the fast condition estimation of the generalized Sylvester equation,which requires O(m2n+mn2) flops,comparing with O(m3+n3) flops for the generalized Schur and generalized HessenbergSchur methods for solving the generalized Sylvester equation.Numerical examples illustrate the sharpness of our perturbation bounds.
基金
supported by National Natural Science Foundation of China(Grant Nos.11001045,10926107 and 11271084)
Specialized Research Fund for the Doctoral Program of Higher Education of MOE(Grant No. 20090043120008)
Training Fund of NENU’S Scientific Innovation Project of Northeast Normal University(Grant No. NENU-STC08009)
Program for Changjiang Scholars and Innovative Research Team in University
the Programme for Cultivating Innovative Students in Key Disciplines of Fudan University(973 Program Project)(Grant No. 2010CB327900)
Doctoral Program of the Ministry of Education(Grant No.20090071110003)
Shanghai Science & Technology Committee and Shanghai Education Committee(Dawn Project)
