The two-grid algorithm confronts a shifted unitary orthogonal method

TL;DR

This paper introduces the Shifted Unitary Orthogonal Method (SUOM), a new Krylov solver for shifted unitary matrices, and demonstrates that a two-grid algorithm significantly improves inversion efficiency over SUOM for the overlap operator.

Contribution

The paper presents a novel optimal Krylov solver for shifted unitary matrices and shows that a two-grid algorithm can outperform SUOM in inverting the overlap operator.

Findings

Two-grid algorithm achieves large gains over SUOM.

Overlap operator can be inverted by successive inversions of the truncated operator.

SUOM serves as a benchmark for evaluating improvements.

Abstract

In this paper I describe a new optimal Krylov subspace solver for shifted unitary matrices called the Shifted Unitary Orthogonal Method (SUOM). This algorithm is used as a benchmark against any improvement like the two-grid algorithm. I use the latter to show that the overlap operator can be inverted by successive inversions of the truncated overlap operator. This strategy results in large gains compared to SUOM.