Efficient tridiagonal preconditioner for the matrix-free truncated Newton method

摘要

In this paper, we study an efficient tridiagonal preconditioner, based on the directional differentiation, applied to the matrix-free truncated Newton method for unconstrained optimization. It is proved that this preconditioner is positive definite for many practical problems. The efficiency of the resulting matrix-free truncated Newton method is demonstrated by results of extensive numerical experiments.