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Projection methods for large-scale T-Sylvester equations
- Source :
- e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid, instname
- Publication Year :
- 2015
- Publisher :
- American Mathematical Society, 2015.
-
Abstract
- The matrix Sylvester equation for congruence, or T-Sylvester equation, has recently attracted considerable attention as a consequence of its close relation to palindromic eigenvalue problems. The theory concerning T-Sylvester equations is rather well understood and there are stable and e cient numerical algorithms which solve these equations for small- to medium-sized matrices. However, developing numerical algorithms for solving large-scale T-Sylvester equations still remains an open problem. In this paper, we present several projection algorithms based on di erent Krylov spaces for solving this problem when the right-hand side of the T-Sylvester equation is a low-rank matrix. The new algorithms have been extensively tested, and the reported numerical results show that they work very well in practice, o ering a clear guidance on which algorithm is the most convenient in each situation. This work has been supported by Ministerio de Economía y Competitividad of Spain through grant MTM2012-32542. Publicado
- Subjects :
- Iterative method
Matemáticas
MathematicsofComputing_NUMERICALANALYSIS
010103 numerical & computational mathematics
01 natural sciences
Krylov subspace
Projection (linear algebra)
Matrix (mathematics)
large-scale equations
Simultaneous equations
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
Applied mathematics
Matrix equations
0101 mathematics
Eigenvalues and eigenvectors
Mathematics
Algebra and Number Theory
Independent equation
Matrix equation
Applied Mathematics
Mathematical analysis
010101 applied mathematics
Computational Mathematics
matrix equations
Sylvester equation
Large-scale equation
Sylvester equation for congruence
Computational Mathematic
iterative methods
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid, instname
- Accession number :
- edsair.doi.dedup.....790c6163748ea763f3e65d30823792c2