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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Summary: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 for solving systems of nonlinear equations. These results are extended to the degenerate case. Examples of applying the results are given.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542513120051