Fractional Inversion in Krylov Space

Details Fractional Inversion in Krylov Space Fractional Inversion in Krylov Space

1998-05-28

arxiv.org/abs/hep-lat/9805030v1

Nucl.Phys.Proc.Suppl.63B:952,1998

Physics

High Energy Physics

High Energy Physics - Lattice

Contribution to LAT97 proceedings, 3 pages

Scientific paper

10.1016/S0920-5632(97)00952-3

The fractional inverse $M^{-\gamma}$ (real $\gamma >0$) of a matrix $M$ is expanded in a series of Gegenbauer polynomials. If the spectrum of $M$ is confined to an ellipse not including the origin, convergence is exponential, with the same rate as for Chebyshev inversion. The approximants can be improved recursively and lead to an iterative solver for $M^\gamma x = b$ in Krylov space. In case of $\gamma = 1/2$, the expansion is in terms of Legendre polynomials, and rigorous bounds for the truncation error are derived.

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