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.

References in corpus (4)

• Optical Solitary Waves in the Higher Order Nonlinear Schrodinger Equation
• Krylov Subspace Recycling for Sequences of Shifted Linear Systems
• Numerical bifurcation study of superconducting patterns on a square
• An optimal linear solver for the Jacobian system of the extreme type-II Ginzburg--Landau problem

Cited by in corpus (1)

• Automatic exploration techniques for the numerical bifurcation study of the Ginzburg-Landau equation