AMG Preconditioned Conjugate Gradient Type Methods

for Nonsymmetric Eigenproblems

nishida@is.s.u-tokyo.ac.jp

Department of Computer Science, Univerisity of Tokyo

7-3-1, Hongo, Bunkyo-ku, Tokyo

113-0033 JAPAN

Akira Nishida

Abstract

When we need to compute the eigenvalues of a large sparse matrix numerically, the projection method such as the Lanczos type or the Davidson type methods has been the most orthodox choice. However, recent studies revealed that the conjugate gradient method combined with appropriate preconditioners can compute a few eigenpairs of such problems quite efficiently. For large scale nonsymmetric eigenproblems, we expand this approach to the conjugate residual and the bi-conjugate gradient type methods, and evaluate the combination with the AMG preconditioner.