Approximation of solution curves of undetermined systems of nonlinear equations
type: Item
instance of: scholarly article
title: Approximation of solution curves of undetermined systems of nonlinear equations
zbMATH Open document ID: 0890.65051
DOI: 10.1007/BF02684413
author: Rolf Neubert
published in: Computing
publication date: 1998-07-06T00:00:00Z
review text: The author investigates the solutions of the underdetermined system of nonlinear equations \[ f(y)= 0,\;f: \mathbb{R}^n \to\mathbb{R}^{n-1} \text{ sufficiently smooth, } n\geq 2. \tag{1} \] The vector \(y\) consists of a vector of state variables \(\widetilde y\in \mathbb{R}^{n-1}\) and a real parameter \(\lambda\). Branching solutions of (1) may be computed using standard continuation or predictor-corrector techniques. The suggested method is based on a functional predictor-corrector principle: operators, which correct interatively the given predictor functions into the wanted neighborhood are constructed. The numerical realization of these techniques strongly depends on the different choices of the operators. Here spline collocation continuation is explained to illustrate the principle of the method.
Mathematics Subject Classification ID: 65H17
Mathematics Subject Classification ID: 65H20
zbMATH DE Number: 1112324
zbMATH Keywords: Picard iteration
zbMATH Keywords: underdeterminated system of nonlinear equations
zbMATH Keywords: functional predictor-corrector principle
zbMATH Keywords: spline collocation continuation
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02684413
OpenAlex ID: W1994543038
description: scientific article; zbMATH DE number 1112324