Fast fermion Monte Carlo

Forcrand, Philippe de; Takaishi, Tetsuya

doi:10.1016/s0920-5632(96)00829-8

Cited by 58 publications

(61 citation statements)

References 4 publications

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“…Relatively recently the Polynomial [20,21] and Rational [22][23][24] Hybrid Monte Carlo algorithms have been developed. These permit the simulation of fractional powers of the fermion determinant without any concomitant systematic errors in the equilibrium distribution.…”

Section: Phmc and Rhmcmentioning

confidence: 99%

“…It is not necessary to use the optimal approximation, but doing so leads to surprisingly small errors; for example, if we consider rational approximations to sgn(x) of degree (21,20) then the optimal Qebyxev/Zolotarev approximation has a maximum error of 4.38 × 10 −3 over 10 −6 ≤ |x| ≤ 1, whereas the Higham rational approximation of the same order, tanh(20 tanh −1 x), clearly has a maximum error of about 1.…”

Section: Qebyxev Approximationmentioning

confidence: 99%

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Algorithms for Lattice QCD with Dynamical Fermions

Kennedy

2005

Nuclear Physics B - Proceedings Supplements

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We consider recent progress in algorithms for generating gauge field configurations that include the dynamical effects of light fermions. We survey what has been achieved in recent state-of-the-art computations, and examine the trade-offs between performance and control of systematic errors. We briefly review the use of polynomial and rational approximations in Hybrid Monte Carlo algorithms, and some of the theory of on-shell chiral fermions on the lattice. This provides a theoretical framework within which we compare algorithmic alternatives for their implementation; and again we examine the trade-offs between speed and error control.

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Section: Phmc and Rhmcmentioning

confidence: 99%

Section: Qebyxev Approximationmentioning

confidence: 99%

Algorithms for Lattice QCD with Dynamical Fermions

Kennedy

2005

Nuclear Physics B - Proceedings Supplements

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“…Some thought may have to be given, however, to which is the best way to include the strange sea quark, although this quark is so heavy that one may be able to do with a preconditioned PHMC algorithm [37,38].…”

Section: Pos(lat2005)002mentioning

confidence: 99%

Lattice QCD with light Wilson quarks

Lüscher¹

2005

Proceedings of XXIIIrd International Symposium on Lattice Field Theory — PoS(LAT2005)

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Wilson's formulation of lattice QCD is attractive for many reasons, but perhaps mainly because of its simplicity and conceptual clarity. Numerical simulations of the Wilson theory (and of its improved versions) tend to be extremely demanding, however, to the extent that they rapidly become impractical at small quark masses. Recent advances in simulation algorithms now allow such simulations to be pushed to significantly smaller masses without having to compromise in other ways. Contact with chiral perturbation theory can thus be made and many physics questions can be addressed that previously appeared to be inaccessible.

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“…In Ref. [24], it was noted that the even-odd matrix itself can be ILU factorised again, and this both accelerates matrix inversion and improves the Metropolis acceptance rate.…”

Section: Ilu Preconditioningmentioning

confidence: 99%