# Comparison of Inversion Algorithms for Wilson Fermions on the CM5

## TL;DR

This paper compares iterative algorithms like MR, CG, BiCGγ₅, and BiCGStab for inverting the Wilson fermion Dirac matrix on the CM-5, finding preconditioned over-relaxed MR and BiCGStab to be most effective and robust.

## Contribution

It provides a comparative analysis of various iterative inversion algorithms for Wilson fermions on the CM-5, highlighting the efficiency and robustness of preconditioned over-relaxed MR and BiCGStab.

## Key findings

- Preconditioned over-relaxed MR is simple, memory-efficient, and comparable to BiCGStab in performance.
- MR and BiCGStab are equally robust, insensitive to initial solutions and round-off errors.
- The study was conducted on 32^3×64 lattices with Wilson fermion action, with and without clover term.

## Abstract

This talk presents results of a comparitive study of iterative algorithms like minimal residue ($MR$) and conjugate gradient ($CG$, $BiCG\gamma_5$, and \bicgstab) used for inverting the Dirac matrix $M$. The tests were done on the Connection Machine CM-5 using $32^3 \times 64$ lattices. The fermion action used is of Wilson type, both with and without the clover term. The overall conclusion is that preconditioned over-relaxed $MR$ is the simplest, uses the least memory, and is comparable in performance to \bicgstab. We find these two algorithms to be equally robust, $i.e.$ insensitive to the starting solution and to round-off errors.