Krylov subspace methods for solving large Lyapunov equations
SIAM Journal on Numerical Analysis
Oblique Projection Methods for Large Scale Model Reduction
SIAM Journal on Matrix Analysis and Applications
A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
SIAM Journal on Scientific Computing
Solution of the matrix equation AX + XB = C [F4]
Communications of the ACM
Low Rank Solution of Lyapunov Equations
SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
On the reflexive and anti-reflexive solutions of the generalised coupled Sylvester matrix equations
International Journal of Systems Science
Extended Arnoldi methods for large low-rank Sylvester matrix equations
Applied Numerical Mathematics
The Lanczos Method for Parameterized Symmetric Linear Systems with Multiple Right-Hand Sides
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
An efficient algorithm for solving general coupled matrix equations and its application
Mathematical and Computer Modelling: An International Journal
| Hi-index | 0.00 |
In this paper we construct an approximate solution to large Sylvester equations of the form AX+XB=CD^T. The construction uses a new variant of the block Arnoldi algorithm which exploits the near-breakdowns, that is, the near singularities in the generated basis. As a consequence, the algorithm eliminates the directions which do not contribute to the approximate solution by keeping in the generated basis only the ''active'' vectors detected by a criterion based on the residual associated with the approximate solution. The effectiveness of the proposed algorithm is demonstrated on several examples, including the case where the matrix B has a small or a large size.