English

Deflation Methods in Fermion Inverters

High Energy Physics - Lattice 2008-11-26 v2 Mathematical Physics math.MP

Abstract

I will review recent developments in matrix deflation methods, by Ronald Morgan/Walter Wilcox, Andreas Stathopoulos/Konstantinos Orginos, and Martin L\"uscher, with application to lattice QCD fermion inversion. I will begin with a short review of deflation-related work in the field. The Morgan/Wilcox algorithms using GMRES and BiCGStab for deflation will be described. Typical results for quenched (Wilson and twisted mass) and dynamical configurations (CP-PACS and ETMC) will be displayed and discussed. I will outline how inclusion of multiple right-hand sides and multiple shifts can be accommodated within versions of these methods. I will also review deflation methods based on Conjugate Gradient introduced by Stathopoulos and Orginos for hermitian systems with multiple right-hand sides as well as L\"uscher's non-hermitian domain decomposition algorithm using Generalized Conjugate Residual.}

Keywords

Cite

@article{arxiv.0710.1813,
  title  = {Deflation Methods in Fermion Inverters},
  author = {Walter Wilcox},
  journal= {arXiv preprint arXiv:0710.1813},
  year   = {2008}
}

Comments

20 pages, 13 figures, 1 table, plenary talk presented at the XXV International Symposium on Lattice Field Theory, 30 July - 4 August 2007, Regensburg, Germany; clarifications made and typos corrected

R2 v1 2026-06-21T09:29:10.533Z