Shifted unitary orthogonal methods for the overlap inversion

TL;DR

This paper compares the convergence of shifted unitary orthogonal methods and Krylov solvers for overlap fermion propagator computations, introducing a new optimized algorithm that outperforms existing methods.

Contribution

It introduces a new geometric optimality-enhanced SUOM algorithm that converges faster than SUMR for overlap fermion propagator calculations.

Findings

SUOM performs similarly to SUMR in convergence.

SUMR converges slightly faster than SUOM.

The new geometric optimality SUOM outperforms SUMR.

Abstract

In this work we compare the convergence of the shifted unitary orthogonal method (SUOM) and different Krylov subspace solvers for propagator computations with overlap fermions. We show that the SUOM algorithm performs similarly to the shifted unitary minimal residual method (SUMR) with the latter converging slightly faster. When the geometric optimality is applied to SUOM we get e new algorithm which is faster than SUMR.