%0 Journal Article
%A van den Eshof, J.
%A Frommer, A.
%A Lippert, Th.
%A Schilling, K.
%A van der Vorst, H. A.
%T Numerical methods for the QCDd overlap operator. I. Sign-function and error bounds
%J Computer physics communications
%V 146
%N 2
%@ 0010-4655
%C Amsterdam
%I North Holland Publ. Co.
%M FZJ-2019-01075
%P 203 - 224
%D 2002
%X 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.
%F PUB:(DE-HGF)16
%9 Journal Article
%R 10.1016/S0010-4655(02)00455-1
%U https://juser.fz-juelich.de/record/860300