Krylov subspace methods for the generalized Sylvester equation q Liang Bao a , Yiqin Lin b , Yimin Wei c, * a Department of Mathematics, Fudan University, Shanghai 200433, PR China b School of Mathematics and Computational Science, Zhongshan University, Guangzhou 510275, PR China c Department of Mathematics, Fudan University, Shanghai 200433, PR China Abstract In the paper we propose Galerkin and minimal residual methods for iteratively solv- ing generalized Sylvester equations of the form AXB  X = C. The algorithms use Krylov subspace for which orthogonal basis are generated by the Arnoldi process and reduce the storage space required by using the structure of the matrix. We give some convergence results and present numerical experiments for large problems to show that our methods are efficient. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Galerkin method; Generalized Sylvester equation; Minimal residual method; Krylov subspace 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.07.041 q This work is supported by NSFC project 10471027 and Shanghai Education Commission. * Corresponding author. E-mail addresses: 021018035@fudan.edu.cn (L. Bao), yiqinlin@hotmail.com (Y. Lin), ymwei@fudan.edu.cn (Y. Wei). Applied Mathematics and Computation 175 (2006) 557–573 www.elsevier.com/locate/amc