Inversion of the fermion matrix and the equivalence of the conjugate gradient and Lanczos algorithms

The Lanczos and conjugate gradient algorithms are widely used in lattice QCD calculations. The previously known close relationship between the two methods is explored and two commonly used implementations are shown to give identically the same results at each iteration, in exact arithmetic, for matr...

Full description

Saved in:
Bibliographic Details
Published in:Computer physics communications 1990-07, Vol.59 (3), p.447-454
Main Authors: Burkitt, A.N., Irving, A.C.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical methods in physics
Numerical approximation and analysis
Physics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The Lanczos and conjugate gradient algorithms are widely used in lattice QCD calculations. The previously known close relationship between the two methods is explored and two commonly used implementations are shown to give identically the same results at each iteration, in exact arithmetic, for matrix inversion. The identities between the coefficients of the two algorithms are given, and many of the features of the two algorithms can now be combined. The effects of finite arithmetic are investigated and the particular Lanczos formulation is found to be most stable with respect to rounding errors.
ISSN:0010-4655
1879-2944
DOI:10.1016/0010-4655(90)90086-G