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On the convergence of inexact Newton method. (Chinese. English summary) Zbl 1040.65045
Summary: Local convergence of the inexact Newton method is discussed. Under the supposition that the semi-continuous second Fréchet derivative \(f''(t)\) satisfies a modified first order-\(\gamma\) condition, its second order convergence is studied and error estimates are obtained. Instead of a stronger condition, a weaker condition is used here. Error estimates of the radius of convergence are given.

MSC:
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47J25 Iterative procedures involving nonlinear operators
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