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On a class of iterative procedures for solving nonlinear equations in Banach spaces

Florian-Alexandru Potra — 1984

Banach Center Publications

An application of the induction method of V. Pták to the study of regula falsi

Florian-Alexandru Potra — 1981

Aplikace matematiky

In this paper we introduce the notion of " $p$ -dimensional rate of convergence" which generalizes the notion of rate of convergence introduced by V. Pták. Using this notion we give a generalization of the Induction Theorem of V. Pták, which may constitute a basis for the study of the iterative procedures of the form $X_{n + 1} = F (x_{n - p + 1}, X_{n - p + 2}, ..., x_{n})$ , $n = 0, 1, 2, ...$ . As an illustration we apply these results to the study of the convergence of the secant method, obtaining sharp estimates for the errors at each step of the iterative procedure.

The rate of convergence of a modified Newton's process

Florian-Alexandru Potra — 1981

Aplikace matematiky

Nondiscrete induction and an inversion-free modification of Newton's method

Florian-Alexandru Potra; Vlastimil Pták — 1983

Časopis pro pěstování matematiky

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