Improving the low-lying spectrum of the overlap kernel

The action of the overlap-Dirac operator on a vector is typically implemented in directly through a multi-shift conjugate gradient solver. The compute-time this takes to evaluate depends upon the condition number $κ$ of the matrix that is used as the overlap kernel. We examine the low-lying spectra of various candidate kernels in an effort to optimise $κ$, thereby speeding up the overlap evaluation.

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