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A note on the Kantorovich theorem for Newton iteration. (English) Zbl 0782.65071

The paper discusses the convergence of the Newton method for a nonsingular solution of the nonlinear equation \(f(x) = 0\) with \(f: X \to Y\) two times differentiable and \(X\), \(Y\) are Banach spaces. Based on the information of the second derivatives of \(f\) at the initial point, the author gives a new criterion for the convergence of the Newton iteration.
Reviewer: Z.Mei (Marburg)

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
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References:

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