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arXiv · hep-lat/0202025

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

J. van den Eshof·A. Frommer·Th. Lippert·K. Schilling·H. A. van der Vorst
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Abstract

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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J. van den Eshof, A. Frommer, Th. Lippert, K. Schilling, H. A. van der Vorst. 2002-02-25. Numerical Methods for the QCD Overlap Operator: I. Sign-Function and Error Bounds. https://doi.org/10.1016/s0010-4655(02)00455-1

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