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

Potra, Florian-Alexandru. "An application of the induction method of V. Pták to the study of regula falsi." Aplikace matematiky 26.2 (1981): 111-120. <http://eudml.org/doc/15187>.

@article{Potra1981,
abstract = {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.},
author = {Potra, Florian-Alexandru},
journal = {Aplikace matematiky},
keywords = {induction method; regula falsi; $p$-dimensional rate of convergence; secant method; iterative procedure; induction method; regula falsi; p-dimensional rate of convergence; secant method; iterative procedure},
language = {eng},
number = {2},
pages = {111-120},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An application of the induction method of V. Pták to the study of regula falsi},
url = {http://eudml.org/doc/15187},
volume = {26},
year = {1981},
}

TY - JOUR
AU - Potra, Florian-Alexandru
TI - An application of the induction method of V. Pták to the study of regula falsi
JO - Aplikace matematiky
PY - 1981
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 26
IS - 2
SP - 111
EP - 120
AB - 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.
LA - eng
KW - induction method; regula falsi; $p$-dimensional rate of convergence; secant method; iterative procedure; induction method; regula falsi; p-dimensional rate of convergence; secant method; iterative procedure
UR - http://eudml.org/doc/15187
ER -