Acceleration of inverse subspace iteration with Newton’s method
| Autor: | Miloud Sadkane, Yu. M. Nechepurenko, G. El Khoury |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Mathematical optimization
Iterative method Applied Mathematics Invariant subspace MathematicsofComputing_NUMERICALANALYSIS Krylov subspace Generalized minimal residual method Computational Mathematics symbols.namesake Rate of convergence Power iteration symbols Applied mathematics Newton's method Subspace topology Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 259:205-215 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2013.06.046 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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