# Efficiency of different matrix inversion methods applied to Wilson fermions

## TL;DR

This paper evaluates the efficiency and reliability of various conjugate gradient-like matrix inversion methods when applied to Wilson fermions in lattice QED, focusing on CPU time and precision near critical parameters.

## Contribution

It provides a comparative analysis of CG, BiCGstab1, and BiCGstab2 methods in the context of Wilson fermions, highlighting their performance and precision issues.

## Key findings

- BiCGstab methods show improved CPU efficiency over CG.
- Machine precision significantly affects result reliability near critical points.
- Method performance varies depending on proximity to the critical line.

## Abstract

We compare different conjugate gradient -- like matrix inversion methods (CG, BiCGstab1 and BiCGstab2) employing for this purpose the compact lattice quantum electrodynamics (QED) with Wilson fermions. The main goals of this investigation are the CPU time efficiency of the methods as well as the influence of machine precision on the reliability of (physical) results especially close to the 'critical' line $~\kappa_c(\bt)$.