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Band preconditioners for the matrix-free truncated Newton method

Ladislav Luksan(luksan***at***cs.cas.cz)
Ctirad Matonoha(matonoha***at***cs.cas.cz)
Jan Vlcek(vlcek***at***cs.cas.cz)

Abstract: This report is devoted to preconditioning techniques for the matrix-free truncated Newton method. After a review of basic known pproaches, we propose ew results concerning tridiagonal and pentadiagonal preconditioners based on the standard BFGS updates and on numerical differentiation. Furthermore, we present results of extensive numerical experiments serving for the careful comparison of suitable preconditioning techniques and confirming efficiency of the band preconditioners.

Keywords: Unconstrained optimization, large scale optimization, truncated Newton method, matrix-free Newton method, band preconditioners, algorithms.

Category 1: Nonlinear Optimization

Citation: Report V-1079, Institute of Computer Science AS CR, Pod Vodarenskou Vezi 2, 18207 Prague 8, 2010.

Download: [PDF]

Entry Submitted: 11/25/2010
Entry Accepted: 11/25/2010
Entry Last Modified: 11/25/2010

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