Double-pass variants for multi-shift BiCGstab(ell)

TL;DR

This paper introduces a double-pass variant of the BiCGstab(ell) algorithm, improving multi-shift inversions for non-Hermitian kernels like the QCD overlap operator at non-zero chemical potential.

Contribution

It presents a novel double-pass algorithm for BiCGstab(ell), extending Neuberger's double-pass idea to non-Hermitian multi-shift problems in lattice QCD.

Findings

The new method shows competitive performance with existing algorithms.

It effectively handles non-Hermitian kernels in QCD computations.

Performance comparisons demonstrate advantages over partial fraction and Krylov-Ritz methods.

Abstract

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.