Deflation Methods in Fermion Inverters
Abstract
Description
I will review recent developments in matrix deflation methods, by Ronald Morgan/Walter Wilcox, Andreas Stathopoulos/Konstantinos Orginos, and Martin Lüscher, 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 Lüscher's non-hermitian domain decomposition algorithm using Generalized Conjugate Residual.}
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
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