In analogy to Neuberger's double-pass algorithm for the Conjugate Gradient inversion with multi-shifts we introduce a double-pass variant for BiCGstab(ell). One possible application is the overlap operator of QCD at non-zero chemical potential, where the kernel of the sign function is non-Hermitian. The sign function can be replaced by a partial fraction expansion, requiring multi-shift inversions. We compare the performance of the new method with other available algorithms, namely partial fraction expansions with restarted FOM inversions and the Krylov-Ritz method using nested Krylov subspaces.
Cite
@article{arxiv.1010.2592,
title = {Double-pass variants for multi-shift BiCGstab(ell)},
author = {Simon Heybrock},
journal= {arXiv preprint arXiv:1010.2592},
year = {2011}
}
Comments
7 pages, 4 figures, proceedings of the XXVIII International Symposium on Lattice Field Theory, Lattice2010, June 14-19, 2010, Villasimius, Italy