Krylov subspace methods for solving large Lyapunov equations
SIAM Journal on Numerical Analysis
Application of ADI Iterative Methods to the Restoration of Noisy Images
SIAM Journal on Matrix Analysis and Applications
Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
Solution of the matrix equation AX + XB = C [F4]
Communications of the ACM
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Low rank approximate solutions to large Sylvester matrix equations
Applied Mathematics and Computation
Convergence properties of some block Krylov subspace methods for multiple linear systems
Journal of Computational and Applied Mathematics
A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
SIAM Journal on Scientific Computing
Use of near-breakdowns in the block Arnoldi method for solving large Sylvester equations
Applied Numerical Mathematics
Krylov subspace methods for projected Lyapunov equations
Applied Numerical Mathematics
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In this paper, we present two iterative methods for the solution of the low-rank Sylvester equation AX+XB+EF^T=0. These methods are projection methods that use the extended block Arnoldi (EBA) process and the extended global Arnoldi (EGA) process to generate orthonormal bases and F-orthonormal bases of extended Krylov subspaces. For each algorithm, we show how to stop the iterations by computing the residual norm or an upper bound without computing the approximate solution and without using expensive products with the matrices A and B. We also describe how to get the low rank solution of the Sylvester equation in a factored form. Finally, some numerical experiments are presented in order to show the efficiency and robustness of the proposed methods.