The inexact, inexact perturbed, and quasi-Newton methods are equivalent models

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The inexact, inexact perturbed, and quasi-Newton methods are equivalent models

A classical model of Newton iterations which takes into account some error terms is given by the quasi-Newton method, which assumes perturbed Jacobians at each step. Its high convergence orders were characterized by Dennis and Moré [Math. Comp. 28 (1974), 549–560]. The inexact Newton method constitutes another such model, since it assumes that at each step the linear systems are only approximat...

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ژورنال

عنوان ژورنال: Mathematics of Computation

سال: 2004

ISSN: 0025-5718

DOI: 10.1090/s0025-5718-04-01646-1