Preconditioned Recycling Krylov subspace methods for self-adjoint problems
Abstract
The authors propose a recycling Krylov subspace method for the solution of a sequence of self-adjoint linear systems. Such problems appear, for example, in the Newton process for solving nonlinear equations. Ritz vectors are automatically extracted from one MINRES run and then used for self-adjoint deflation in the next. The method is designed to work with arbitrary inner products and arbitrary self-adjoint positive-definite preconditioners whose inverse can be computed with high accuracy. Numerical experiments with nonlinear Schrödinger equations indicate a substantial decrease in computation time when recycling is used.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2012
- DOI:
- 10.48550/arXiv.1208.0264
- arXiv:
- arXiv:1208.0264
- Bibcode:
- 2012arXiv1208.0264G
- Keywords:
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- Mathematics - Numerical Analysis;
- Physics - Computational Physics;
- 65F10;
- 65F08;
- 35Q55;
- 35Q56