pth-order approximation of the solution set of nonlinear equations

Given a system of nonlinear equations, a formula is derived for the family of its approximate solutions of up to the p th order of smallness. A formula approximating an implicit function up to the third order of smallness is presented. Iterative methods converging with the p th order are constructed...

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Bibliographic Details

Published in:	Computational mathematics and mathematical physics Vol. 53; no. 12; pp. 1763 - 1780
Main Authors:	Evtushenko, Yu. G., Tret’yakov, A. A.
Format:	Journal Article
Language:	English
Published:	Boston Springer US 01.12.2013 Springer Nature B.V
Subjects:	Approximation Computational mathematics Computational Mathematics and Numerical Analysis Mathematical analysis Mathematics Mathematics and Statistics Nonlinear equations Studies nonlinear equations degenerate case th-order approximations iterative method generalized implicit function theorem
ISSN:	0965-5425, 1555-6662
Online Access:	Get full text
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