Linear systems solvers — recent developments and implications for lattice computations

1996/08/14 by Andreas Frommer
Computer Science · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Matrix Theory and Algorithms #Numerical methods for differential equations #hep-lat

paper · pdf · doi:10.1016/s0920-5632(96)00605-6

published as Nucl.Phys.Proc.Suppl. 53 (1997) 120-126 · 7 pages, LaTeX using espcrc2.sty, 2 figures, 9 eps-files, Talk presented at LATTICE96(algorithms), submitted to Nucl. Phys. B, Proc. Suppl

arxiv created 1996/08/14 · openalex publication_date 1997/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review the numerical analysis' understanding of Krylov subspace methods for solving (non-hermitian) systems of equations and discuss its implications for lattice gauge theory computations using the example of the Wilson fermion matrix. Our thesis is that mature methods like QMR, BiCGStab or restarted GMRES are close to optimal for the Wilson fermion matrix. Consequently, preconditioning appears to be the crucial issue for further improvements.

Citations

• Accurate hadron spectroscopy on blocked configurations by tadpole-renormalized, clover-improved Wilson quark action
• Solution of Sparse Indefinite Systems of Linear Equations
• QMR: a quasi-minimal residual method for non-Hermitian linear systems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems