An application of the induction method of V. Pták to the study of regula falsi
Applications of Mathematics, Tome 26 (1981) no. 2, pp. 111-120.

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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 $X_{n+1}=F(x_{n-p+1},X_{n-p+2},\ldots, x_n)$, $n=0,1,2,\ldots$. 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.
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 
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Potra, Florian Alexandru. An application of the induction method of V. Pták to the study of regula falsi. Applications of Mathematics, Tome 26 (1981) no. 2, pp. 111-120. doi : 10.21136/AM.1981.103902. https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1981.103902/

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