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SIAMSC
2008

Fast (Structured) Newton Computations

13 years 3 months ago
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
Thomas F. Coleman, Wei Xu
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2008
Where SIAMSC
Authors Thomas F. Coleman, Wei Xu
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