Preconditioned Recycling Krylov subspace methods for self-adjoint problems

2012/08/01 by André Gaul, Gaul, André, Nico Schlömer +1
Computer Science · Engineering · Physics and Astronomy · #35Q55 #35Q56 #65F08 #65F10 #Computational Physics (physics.comp-ph) #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1208.0264

openalex publication_date 2012/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Solution of Sparse Indefinite Systems of Linear Equations
• Choosing the Forcing Terms in an Inexact Newton Method
• A Note on Preconditioning for Indefinite Linear Systems
• Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities

Related

• Memory-efficient recycling of large Krylov-subspaces for sequences of Hermitian linear systems
• Krylov-subspace recycling via the POD-augmented conjugate-gradient method
• A survey of subspace recycling iterative methods
• Short-Recurrence and -Storage Recycling of large Krylov-Subspaces for Sequences of Linear Systems with changing Right-Hand-Sides
• Unprojected recycled block Krylov subspace methods for shifted systems