Inaccuracy in Quasi-Newton Methods: Local Improvement Theorems

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dc.contributor.authorDennis, J.E. Jr.en_US
dc.contributor.authorWalker, Homer F.en_US
dc.date.accessioned2018-06-18T17:23:11Zen_US
dc.date.available2018-06-18T17:23:11Zen_US
dc.date.issued1983-03en_US
dc.date.noteMarch 1983en_US
dc.description.abstractIn this paper, we consider the use of bounded-deterioration quasi-Newton methods implemented in floating-point arithmetic to find solutions to F(x)=0 where only inaccurate F-values are available. Our analysis is for the case where the relative error in F is less than one. We obtain theorems specifying local rates of improvement and limiting accuracies depending on the nearness to Newton's method of the basic algorithm, the accuracy of its implementation, the relative errors in the function values, the accuracy of the solutions of the linear systems for the Newton steps, and the unit-rounding errors in the addition of the Newton steps.en_US
dc.format.extent30 ppen_US
dc.identifier.citationDennis, J.E. Jr. and Walker, Homer F.. "Inaccuracy in Quasi-Newton Methods: Local Improvement Theorems." (1983) <a href="https://hdl.handle.net/1911/101552">https://hdl.handle.net/1911/101552</a>.en_US
dc.identifier.digitalTR83-11en_US
dc.identifier.urihttps://hdl.handle.net/1911/101552en_US
dc.language.isoengen_US
dc.titleInaccuracy in Quasi-Newton Methods: Local Improvement Theoremsen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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