Efficient Tridiagonal Preconditioner for the Matrix-Free Truncated Newton Method

Authors: Ladislav Lukšan, Jan Vlček
Publication year: 2014
Publication type: Článek v odborném periodiku
Periodical: Applied Mathematics and Computation
Projects: Iterative Methods in Computational Mathematics: Analysis, Preconditioning, and Applications
Bibliographic citation: LUKŠAN, Ladislav, VLČEK, Jan. Efficient Tridiagonal Preconditioner for the Matrix-Free Truncated Newton Method. Applied Mathematics and Computation. 2014, 235(25 May), 394-407. ISSN 0096-3003. E-ISSN 1873-5649
Dostupné z: doi:10.1016/j.amc.2014.03.006
DOI: 10.1016/j.amc.2014.03.006
ID: 427366

Abstract

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.