An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems
Gene Howard Golub, Qiang John Ye · SIAM Journal on Scientific Computing · 2002
In this paper, we present an inverse free Krylov subspace method for finding some extreme eigenvalues of the symmetric definite generalized eigenvalue problem $Ax = \lambda B x$. The basic method takes a form of inner-outer iterations and involves no inversion of B or any shift-and-invert matrix $A-\lambda_0 B$. A convergence analysis is presented that leads to a preconditioning scheme for accelerating convergence through some equivalent transformations of the eigenvalue problem. Numerical examples are given to illustrate the convergence properties and to demonstrate the competitiveness of the method.