出版社:SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要:A deflated and restarted Lanczos algorithm to solve hermitian linear systems, and at the same
time compute eigenvalues and eigenvectors for application to multiple right-hand sides, is described.
For the first right-hand side, eigenvectors with small eigenvalues are computed while
simultaneously solving the linear system. Two versions of this algorithm are given. The first is
called Lan-DR and is based on conjugate gradient (CG) implementation of the Lanczos algorithm.
This version will be optimal for the hermitian positive definite case. The second version is called
MinRes-DR and is based on the minimum residual (MinRes) implementation of Lanczos algorithm.
This version is optimal for indefinite hermitian systems where the CG algorithm is subject
to instabilities. For additional right-hand sides, we project over the calculated eigenvectors to
speed up convergence. The algorithms used for subsequent right-hand sides are called D-CG and
D-MinRes respectively. After some introductory examples are given, we show tests for the case
of Wilson fermions at kappa critical. A considerable speed up in the convergence is observed
compared to unmodified CG and MinRes.