Showing papers by "Vlastimil Pták published in 1980"
TL;DR: The method of nondiscrete mathematical induction is applied to the Newton process and yields a very simple proof of the convergence and sharp apriori estimates.
Abstract: The method of nondiscrete mathematical induction is applied to the Newton process. The method yields a very simple proof of the convergence and sharp apriori estimates; it also gives aposteriori bounds which are, in general, better than those given in [1].
91 citations
TL;DR: In this article, a connected account of results concerning the maximum problem raised by the first-named author in [21] and of its generalizations is given, simplified proofs are given, new estimates are obtained, and important connections with stability theory and with classical function theory are pointed out.
28 citations
TL;DR: In this article, the method of non-discrete mathematical induction is applied to the multistep Newton method and optimal conditions for convergence as well as estimates, sharp for the whole length of the process, are obtained.
Abstract: The method of nondiscrete mathematical induction is applied to the multistep Newton method. Optimal conditions for convergence as well as estimates, sharp for the whole length of the process, are obtained.
15 citations
TL;DR: In this paper, the method of non-discrete mathematical induction is applied to a multistep variant of the secant method and optimal conditions for convergence as well as error estimates are obtained.
Abstract: The method of nondiscrete mathematical induction is applied to a multistep variant of the secant method. Optimal conditions for convergence as well as error estimates, sharp in every step, are obtained.
13 citations