Preconditioning the non-relativistic many-fermion problem

Details Preconditioning the non-relativistic many-fermion problem Preconditioning the non-relativistic many-fermion problem

2010-08-21

arxiv.org/abs/1008.3647v1

Physics

High Energy Physics

High Energy Physics - Lattice

12 pages, 1 figure

Scientific paper

Preconditioning is at the core of modern many-fermion Monte Carlo algorithms, such as Hybrid Monte Carlo, where the repeated solution of a linear problem involving an ill-conditioned matrix is needed. We report on a performance comparison of three preconditioning strategies, namely Chebyshev polynomials, strong-coupling approximation and weak-coupling expansion. We use conjugate gradient (CG) on the normal equations as well as stabilized biconjugate gradient (BiCGStab) as solvers and focus on the fermion matrix of the unitary Fermi gas. Our results indicate that BiCGStab is by far the most efficient strategy, both in terms of the number of iterations and matrix-vector operations.

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