A truncated - CG style method for symmetric generalized eigenvalue problems 1

A numerical algorithm is proposed for computing an extreme eigenpair of a symmetric/positive-definite matrix pencil (A, B). The leftmost or the rightmost eigenvalue can be targeted. Knowledge of (A, B) is only required through a routine that performs matrix-vector products. The method has excellent global convergence properties and its local rate of convergence is superlinear. It is based on a constrained truncated-CG trust-region strategy to optimize the Rayleigh quotient, in the framework of a recently-proposed trust-region scheme on Riemannian manifolds.