Comparison of Inversion Algorithms for Wilson Fermions on the CM5

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, $i\mathrm{.}e\mathrm{.}$ insensitive to the starting solution and to round-off errors.