Volume 44, pp. 522-547, 2015.

Preconditioned Recycling Krylov subspace methods for self-adjoint problems

André Gaul and Nico Schlömer


A recycling Krylov subspace method for the solution of a sequence of self-adjoint linear systems is proposed. 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.

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Key words

Krylov subspace methods, MINRES, deflation, Ritz vector recycling, nonlinear Schrödinger equations, Ginzburg–Landau equations

AMS subject classifications

65F10, 65F08, 35Q55, 35Q56

ETNA articles which cite this article

Vol. 45 (2016), pp. 499-523 Kirk M. Soodhalter: Two recursive GMRES-type methods for shifted linear systems with general preconditioning

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