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dc.contributor.authorDennis, John E., Jr.en_US
dc.contributor.authorSchnabel, Robert B.en_US
dc.date.accessioned2007-04-23T18:21:44Z
dc.date.available2007-04-23T18:21:44Z
dc.date.issued1978-06en_US
dc.identifier.citationhttp://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR78-344en_US
dc.identifier.urihttps://hdl.handle.net/1813/7463
dc.description.abstractIn many problems involving the solution of a system of nonlinear equations, it is necessary to keep an approximation to the Jacobian matrix which is updated at each iteration. Computational experience indicates that the best updates are those that minimize some reasonable measure of the change to the current Jacobian approximation subject to the new approximation obeying a secant condition and perhaps some other approximation properties such as symmetry. In this paper we extend the affine case of a theorem of Cheney and Goldstein on proximity maps of convex sets to show that a generalization of the symmetrization technique of Powell always generates least change updates. This generalization has such broad applicability that we obtain an easy unified derivation of all the most successful updates. Furthermore, our techniques apply to interesting new cases such as when the secant condition might be inconsistent with some essential approximation property like sparsity. We also offer advice on how to choose the properties which are to be incorporated into the approximations and how to choose the measure of changes to be minimized.en_US
dc.format.extent1409883 bytes
dc.format.extent448970 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/postscript
dc.language.isoen_USen_US
dc.publisherCornell Universityen_US
dc.subjectcomputer scienceen_US
dc.subjecttechnical reporten_US
dc.titleLeast Change Secant Updates for Quasi-Newton Methodsen_US
dc.typetechnical reporten_US


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