Preconditioned Recycling Krylov subspace methods for self-adjoint problems
This work addresses the need for efficient solvers for sequences of self-adjoint linear systems, which arise in Newton-type methods for nonlinear problems.
The authors propose a recycling Krylov subspace method for solving sequences of self-adjoint linear systems, using Ritz vectors from one MINRES run to deflate the next. Numerical experiments on nonlinear Schrödinger equations show a substantial decrease in computation time.
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.