zbMATH — the first resource for mathematics

On Newton’s method and nondiscrete mathematical induction. (English) Zbl 0642.65043
The author considers the equation (1) \(F(x)=0\) where F is a nonlinear operator from a Banach space E into itself. The method of nondiscrete mathematical induction is used to find sharp error bounds for Newton’s method. It is assumed that the operator F has Hölder continuous derivatives. When the Fréchet-derivative of the operator F satisfies a Lipschitz condition the obtained results reduced to the ones obtained by Ptak and Potra in 1972.
Reviewer: O.Hadžić

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
Full Text: DOI
[1] Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (1970) · Zbl 0241.65046
[2] DOI: 10.1137/0705003 · Zbl 0155.46701
[3] Rheinboldt, Numerical Analysis of Parametrized Nonlinear Equations (1986)
[4] Davis, Introduction to Nonlinear Differential and Integral Equations (1962)
[5] Potra, Nondiscrete Induction and Iterative Processes (1984)
[6] Kantorovich, Functional Analysis in Normed Spaces (1964)
[7] DOI: 10.1007/BF01463998 · Zbl 0434.65034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.