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

Aplikace matematiky (1981)

- Volume: 26, Issue: 2, page 111-120
- ISSN: 0862-7940

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topPotra, 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 -

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