Calculation of eigenvalues and eigenvectors for large sparse non-Herimitian matrices in lattice QCD
Speaker: Hiroya Suno (RIKEN)
Date: Thursday, 3 December 2015, 15:30-17:00
Session: Numerics I
Talk type: Short talk (15 min)
Abstract: We are developing a computer code to find eigenvalues and eigenvectors of large sparse non-Hermitian matrices arising in lattice quantum chromodynamics (lattice QCD). We adopt here a method based on a contour integral, called the Sakurai-Sugiura (SS) method, in order to obtain desired eigenvalues located inside a given contour of the complex plane. We apply the method to calculating several low-lying eigenvalues of the non-Hermitian O(a)-improved Wilson-Dirac operator. Our implementation is tested for the Wilson-Dirac operator in free case, for which the eigenvalues are analytically known. We also carry out several numerical experiments using different sets of gauge field configurations obtained in quenched approximation as well as in full QCD simulation almost at the physical point. Various lattice sizes LxLyLzLt are considered from 83x16 to 964, amounting to the matrix order 12LxLyLzLt from 98,304 to 1,019,215,872.