Deflation of Eigenvalues for Iterative Methods in Lattice QCD

TL;DR

This paper extends and analyzes deflated GMRES algorithms for lattice QCD, focusing on multi-mass and multi-right-hand side implementations to improve computational efficiency.

Contribution

It introduces a multi-mass extension of deflated GMRES and a combined approach with deflated BiCGStab for multiple right-hand sides in lattice QCD.

Findings

Multi-mass deflated GMRES implementation demonstrated.

Efficient solution for multiple right-hand sides shown.

Numerical results support the proposed methods.

Abstract

Work on generalizing the deflated, restarted GMRES algorithm, useful in lattice studies using stochastic noise methods, is reported. We first show how the multi-mass extension of deflated GMRES can be implemented. We then give a deflated GMRES method that can be used on multiple right-hand sides of $Ax=b$ in an efficient manner. We also discuss and give numerical results on the possibilty of combining deflated GMRES for the first right hand side with a deflated BiCGStab algorithm for the subsequent right hand sides.