Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2009-12-22
Comput.Phys.Commun.182:878-889,2011
Physics
High Energy Physics
High Energy Physics - Lattice
17 pages, 12 figures, minor corrections, extended analysis of the preconditioning step
Scientific paper
10.1016/j.cpc.2010.09.022
We present an acceleration of the well-established Krylov-Ritz methods to compute the sign function of large complex matrices, as needed in lattice QCD simulations involving the overlap Dirac operator at both zero and nonzero baryon density. Krylov-Ritz methods approximate the sign function using a projection on a Krylov subspace. To achieve a high accuracy this subspace must be taken quite large, which makes the method too costly. The new idea is to make a further projection on an even smaller, nested Krylov subspace. If additionally an intermediate preconditioning step is applied, this projection can be performed without affecting the accuracy of the approximation, and a substantial gain in efficiency is achieved for both Hermitian and non-Hermitian matrices. The numerical efficiency of the method is demonstrated on lattice configurations of sizes ranging from 4^4 to 10^4, and the new results are compared with those obtained with rational approximation methods.
Bloch Jacques C. R.
Heybrock Simon
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