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Acceleration of inverse subspace iteration with Newton’s method.
- Source :
-
Journal of Computational & Applied Mathematics . Mar2014, Vol. 259, p205-215. 11p. - Publication Year :
- 2014
-
Abstract
- Abstract: This work is focused on the computation of the invariant subspace associated with a separated group of eigenvalues near a specified shift of a large sparse matrix. First, we consider the inverse subspace iteration with the preconditioned GMRES method. It guarantees a convergence to the desired invariant subspace but the rate of convergence is at best linear. We propose to use it as a preprocessing for a Newton scheme which necessitates, at each iteration, the solution of a Sylvester type equation for which an iterative algorithm based on the preconditioned GMRES method is specially devised. This combination results in a fast and reliable method. We discuss the implementation aspects and propose a theory of convergence. Numerical tests are given to illustrate our approach. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 259
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 91870545
- Full Text :
- https://doi.org/10.1016/j.cam.2013.06.046