文献类型：期刊文献

英文题名：A projection method based on extended Krylov subspaces for solving Sylvester equations

作者：Lin, Yiqin[1]; Bao, Liang[2]; Wei, Yimin[3,4]

机构：[1] Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Yongzhou 425100, China; [2] Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China; [3] School of Mathematical Sciences, Fudan University, Shanghai 200433, China; [4] Key Laboratory of Mathematics for Nonlinear Sciences [Fudan University], Ministry of Education, China

年份：2011

卷号：55

起止页码：1132

外文期刊名：World Academy of Science, Engineering and Technology

收录：EI(收录号：20125215834984)

语种：英文

外文关键词：Numerical methods - Inverse problems - Matrix algebra

摘要：In this paper we study numerical methods for solving Sylvester matrix equations of the form AX + XBT + CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its in-verse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.