A refined Arnoldi type method for large scale eigenvalue problems

We present a refined Arnoldi-type method for extracting partial eigenpairs of large matrices. The approximate eigenvalues are the Ritz values of (A - tau I)(-1) with respect to a shifted Krylov subspace. The approximate eigenvectors are derived by satisfying certain optimal properties, and they can be computed cheaply by a small sized singular value problem. Theoretical analysis show that the approximate eigenpairs computed by the new method converges as the approximate subspace expands. Finally, numerical results are reported to show the efficiency of the new method.