On certain computable tests and componentwise error bounds
type: Item
instance of: scholarly article
title: On certain computable tests and componentwise error bounds
zbMATH Open document ID: 0784.65050
DOI: 10.1007/BF02243877
published in: Computing
publication date: 1994-04-13T00:00:00Z
review text: The authors give an overview on some existence and uniqueness tests for zeros of nonlinear functions \(f: \mathbb{R}^ n\to\mathbb{R}^ n\). They recall results of \textit{R. E. Moore} and \textit{J. B. Kioustelidis} [SIAM J. Numer. Anal. 17, 521-529 (1980; Zbl 0457.65031)], \textit{M. C. Pandian} [ibid. 22, 779-791 (1985; Zbl 0586.65041)], \textit{L. Qi} [ibid. 19, 851-857 (1982; Zbl 0506.65020)], the first author and \textit{A. Neumaier} [Computing 40, 85-90 (1988; Zbl 0629.65054)], the authors [Nonlinear Anal., Theory Methods Appl. 15, No. 3, 229-232 (1990; Zbl 0727.65045)]. They generalize some of these results, and they compare them in order to find out their quality. This is partly done theoretically and partly by examples.
reviewed by: Günter Mayer
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 425530
zbMATH Keywords: computable tests
zbMATH Keywords: error bounds
zbMATH Keywords: systems of nonlinear equations
zbMATH Keywords: existence test
zbMATH Keywords: uniqueness test
zbMATH Keywords: interval arithmetic
zbMATH Keywords: zeros of nonlinear functions
author: Zuhe Shen
author: Michael A. Wolfe
MaRDI profile type: Publication
cites work: Q3345690
cites work: Perturbation Bounds for Nonlinear Equations
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cites work: Algorithmic error estimation for approximate solutions of nonlinear systems of equations
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cites work: A Note on the Moore Test for Nonlinear Systems
cites work: A note on Moore's interval test for zeros of nonlinear systems
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cites work: A note on the comparison of the Kantorovich and Moore theorems
full work available at URL: https://doi.org/10.1007/bf02243877
OpenAlex ID: W49472775
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description: scientific article; zbMATH DE number 425530