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Title: Přizpůsobení Newtonovy metody k dodatečným nerovnostem pro neznámě (Czech)
Title: Adapting the Newton-Raphson method to additional inequalities for the variables (English)
Author: Liebl, Petr
Language: Czech
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 12
Issue: 6
Year: 1967
Pages: 419-424
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: In the paper there the effect of a substitution $x_i=h_i(z_1,\ldots,z_n),\ i=1,\ldots,n$ on the solution of a system of nonlinear equations $f_i(x_1,\ldots, x_n)=0, i=1,\ldots, n$ by the Newton-Raphson method is investigated. Formulas are derived which make possible the numerical calculation without actually performing the substitution. It is shown, that it is possible to derive formulas which keep the variables $x_i$ within certain bounds. All of them may be understood as the ordinary Newton-Raphson formula for the original system modified by a substitution. (English)
Keyword: numerical analysis
idZBL: Zbl 0168.13206
DOI: 10.21136/AM.1967.103123
Date available: 2008-05-20T17:40:21Z
Last updated: 2020-07-28
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