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000050021 0247_ $$2DOI$$a10.1016/j.cpc.2004.10.005
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000050021 084__ $$2WoS$$aComputer Science, Interdisciplinary Applications
000050021 084__ $$2WoS$$aPhysics, Mathematical
000050021 1001_ $$0P:(DE-HGF)0$$aCundy, N.$$b0
000050021 245__ $$aNumerical Methods for the QCD Overlap Operator. III. Nested Iterations
000050021 260__ $$aAmsterdam$$bNorth Holland Publ. Co.$$c2005
000050021 300__ $$a221 - 242
000050021 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article
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000050021 440_0 $$01439$$aComputer Physics Communications$$v165$$x0010-4655
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000050021 520__ $$aThe numerical and computational aspects of chiral fermions in lattice quantum chromodynamics are extremely demanding. In the overlap framework, the computation of the fermion propagator leads to a nested iteration where the matrix vector multiplications in each step of an outer iteration have to be accomplished by an inner iteration; the latter approximates the product of the sign function of the hermitian Wilson fermion matrix with a vector.In this paper we investigate aspects of this nested paradigm. We examine several Krylov subspace methods to be used as an outer iteration for both propagator computations and the Hybrid Monte-Carlo scheme. We establish criteria on the accuracy of the inner iteration which allow to preserve an a priori given precision for the overall computation. It will turn out that the accuracy of the sign function can be relaxed as the outer iteration proceeds. Furthermore, we consider preconditioning strategies, where the preconditioner is built upon an inaccurate approximation to the sign function. Relaxation combined with preconditioning allows for considerable savings in computational efforts up to a factor of 4 as our numerical experiments illustrate. We also discuss the possibility of projecting the squared overlap operator into one chiral sector. (C) 2004 Elsevier B.V. All rights reserved.
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000050021 65320 $$2Author$$alattice quantum chromodynamics
000050021 65320 $$2Author$$aoverlap fermions
000050021 65320 $$2Author$$amatrix sign function
000050021 65320 $$2Author$$ainner-outer iterations
000050021 65320 $$2Author$$arelaxation
000050021 65320 $$2Author$$aflexible Krylov
000050021 65320 $$2Author$$asubspace methods
000050021 7001_ $$0P:(DE-HGF)0$$aEshof v. d., J.$$b1
000050021 7001_ $$0P:(DE-HGF)0$$aFrommer, A.$$b2
000050021 7001_ $$0P:(DE-Juel1)132171$$aKrieg, S.$$b3$$uFZJ
000050021 7001_ $$0P:(DE-Juel1)132179$$aLippert, T.$$b4$$uFZJ
000050021 7001_ $$0P:(DE-HGF)0$$aSchäfer, K.$$b5
000050021 773__ $$0PERI:(DE-600)1466511-6$$a10.1016/j.cpc.2004.10.005$$gVol. 165, p. 221 - 242$$p221 - 242$$q165<221 - 242$$tComputer physics communications$$v165$$x0010-4655$$y2005
000050021 8567_ $$uhttp://dx.doi.org/10.1016/j.cpc.2004.10.005
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000050021 915__ $$0StatID:(DE-HGF)0010$$aJCR/ISI refereed
000050021 9201_ $$0I:(DE-Juel1)VDB62$$d31.12.2007$$gZAM$$kZAM$$lZentralinstitut für Angewandte Mathematik$$x0
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