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| Home > External Publications > Vita Publications > Numerical methods for the QCDd overlap operator. I. Sign-function and error bounds |
| Home > External Publications > Vita Publications > Numerical methods for the QCDd overlap operator. I. Sign-function and error bounds |
| Journal Article | FZJ-2019-01075 |
; ; ; ;
2002
North Holland Publ. Co.
Amsterdam
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Please use a persistent id in citations: doi:10.1016/S0010-4655(02)00455-1
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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