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arXiv · 1208.0264

Preconditioned Recycling Krylov subspace methods for self-adjoint problems

André Gaul·Nico Schlömer
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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 Schr\"odinger equations indicate a substantial decrease in computation time when recycling is used.

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André Gaul, Nico Schlömer. 2012-08-01. Preconditioned Recycling Krylov subspace methods for self-adjoint problems. https://arxiv.org/abs/1208.0264

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