GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Application of ADI Iterative Methods to the Restoration of Noisy Images
SIAM Journal on Matrix Analysis and Applications
Global FOM and GMRES algorithms for matrix equations
Applied Numerical Mathematics
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
On the ADI method for Sylvester equations
Journal of Computational and Applied Mathematics
Extended Arnoldi methods for large low-rank Sylvester matrix equations
Applied Numerical Mathematics
Convex constrained optimization for large-scale generalized Sylvester equations
Computational Optimization and Applications
Solving large-scale continuous-time algebraic Riccati equations by doubling
Journal of Computational and Applied Mathematics
On the ADI method for the Sylvester equation and the optimal-H2 points
Applied Numerical Mathematics
Large-scale Stein and Lyapunov equations, Smith method, and applications
Numerical Algorithms
Computers & Mathematics with Applications
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In the present paper, we propose an Arnoldi-based method for solving large and sparse Sylvester matrix equations with low rank right hand sides. We will show how to extract low-rank approximations via a matrix Krylov subspace method. We give some theoretical results such an expression of the exact solution and upper bounds for the norm of the error and for the residual. Numerical experiments will also be given to show the effectiveness of the proposed method.