TY  - JOUR
AU  - van den Eshof, J.
AU  - Frommer, A.
AU  - Lippert, Th.
AU  - Schilling, K.
AU  - van der Vorst, H. A.
TI  - Numerical methods for the QCDd overlap operator. I. Sign-function and error bounds
JO  - Computer physics communications
VL  - 146
IS  - 2
SN  - 0010-4655
CY  - Amsterdam
PB  - North Holland Publ. Co.
M1  - FZJ-2019-01075
SP  - 203 - 224
PY  - 2002
AB  - 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.
LB  - PUB:(DE-HGF)16
DO  - DOI:10.1016/S0010-4655(02)00455-1
UR  - https://juser.fz-juelich.de/record/860300
ER  -