Fast (Structured) Newton Computations

Abstract. Many vector-valued functions, representing expensive computations, are also structured computations. In this case the calculation of the Newton step can be greatly accelerated by exploiting this structure. It is often not necessary, nor economic, to form the true Jacobian in the process of computing the Newton step; instead, a more cost-effective auxiliary Jacobian matrix is used. This auxiliary matrix can be sparse even when the true Jacobian matrix is dense; consequently, sparse matrix technology can be used, to great speed advantage, both in forming the auxiliary matrix and in solving the auxiliary linear system. Key words. Newton method, automatic differentiation, Jacobian matrix AMS subject classifications. 65K05, 65K10, 65H10, 90C30, 90C05, 68L10 DOI. 10.1137/070701005

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Thomas F. Coleman, Wei Xu
• Keywords: Auxiliary Jacobian Matrix, Auxiliary Matrix, Jacobian Matrix, SIAMSC 2008