2010/08/21 by Timour Ten, Ten, Timour, Joaquín E. Drut +3
Chemistry · Computer Science · Materials Science · Physics and Astronomy · #Advanced NMR Techniques and Applications #Matrix Theory and Algorithms #X-ray Diffraction in Crystallography #cond-mat.stat-mech #hep-lat #nucl-th
paper · pdf · doi:10.48550/arxiv.1008.3647
12 pages, 1 figure
arxiv created 2010/08/21 · arxiv updated 2010/08/24
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.