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

Potra, Florian Alexandru

Applications of Mathematics, Tome 26 (1981) no. 2, pp. 111-120.

Résumé

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 $X_{n+1}=F(x_{n-p+1},X_{n-p+2},\dots ,x_n)$, $n=0,1,2,\dots$. 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.

Détail

DOI : 10.21136/AM.1981.103902

Classification : 47H17, 49A51, 58C15, 65H10, 65J10
Mots-clés : induction method; regula falsi; $p$-dimensional rate of convergence; secant method; iterative procedure