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Ph (?) Lder Equation, The Inexact Newton Method And Its Convergence

Posted on:2011-01-06Degree:MasterType:Thesis
Country:ChinaCandidate:H SunFull Text:PDF
GTID:2190360302492248Subject:Operational Research and Cybernetics
Abstract/Summary:PDF Full Text Request
We analyze the convergence of the inexact Newton method when the first Frechet derivative of operator involved is Holder continuous. We give some results on the existence and uniqueness of the solution for a nonlinear equation. Based on this study, we calculate also the R-rate of convergence.Inexact Newton method is one of the most popular method for solving optimization problems. Dembo, Eisenstat and Steihang [2] formed the inexact Newton method for the first time. They proved the local convergence of inexact Newton method in [2]. Under the supposition that continuous second Frechet derivative f"(x) satisfied a modified first order y condition, its convergence and the rate of convergence of the inexact Newton method is superlinear were studied and error estimates were obtained. Instead of a stronger condition of the Newton method, a weaker condition was used there. Error estimates of radius of convergence were given.In [6], Hernandez analyzed the convergence of the inexact Newton method when the first Frechet derivative of operator involved is Holder continuous. The author defined one scalar sequence of by two real functions, which was related to the Newton method. He analyzed the scalar sequence was a Cauchy sequence so that the convergence of the sequence of the Newton method was guaranteed. He given some results on the existence and uniqueness of the solution for a nonlinear equation system. Based on this study, furthermore he calculated also the R-rate of convergence. Following this idea, two real functions are introduced in order to prove the local convergence of inexact Newton method, inexact affine scaling quasi-Newton method under the Holder condition.
Keywords/Search Tags:the inexact Newton method, the affine inexact quasi-Newton method, recurrence relation, R-rate of convergence, semilocal convergence theorem
PDF Full Text Request
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