Linear systems solvers - recent developments and implications for lattice computations

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.

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

References in corpus (2)

• Many Masses on One Stroke: Economic Computation of Quark Propagators
• Accurate hadron spectroscopy on blocked configurations by tadpole-renormalized, clover-improved Wilson quark action

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• Tests of Hypercubic Fermion Actions
• Improved Seed Methods for Symmetric Positive Definite Linear Equations with Multiple Right-hand Sides
• Linear Algebra with Disordered Sparse Matrices that have Spatial Structure: Theory and Computation