On a class of iterative procedures for solving nonlinear equations in Banach spaces
The rate of convergence of a modified Newton's process
An application of the induction method of V. Pták to the study of regula falsi
In this paper we introduce the notion of "-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 , . 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.
Nondiscrete induction and an inversion-free modification of Newton's method
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