Numerical Methods for the QCD Overlap Operator: I. Sign-Function and Error Bounds

Details Numerical Methods for the QCD Overlap Operator: I. Sign-Function and Error Bounds Numerical Methods for the QCD Overlap Operator: I. Sign-Function and Error Bounds

2002-02-25

arxiv.org/abs/hep-lat/0202025v1

Comput.Phys.Commun. 146 (2002) 203-224

Physics

High Energy Physics

High Energy Physics - Lattice

30 pages, 2 figures

Scientific paper

10.1016/S0010-4655(02)00455-1

The numerical and computational aspects of the overlap formalism in lattice quantum chromodynamics are extremely demanding due to a matrix-vector product that involves the sign function of the hermitian Wilson matrix. In this paper we investigate several methods to compute the product of the matrix sign-function with a vector, in particular Lanczos based methods and partial fraction expansion methods. Our goal is two-fold: we give realistic comparisons between known methods together with novel approaches and we present error bounds which allow to guarantee a given accuracy when terminating the Lanczos method and the multishift-CG solver, applied within the partial fraction expansion methods.

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