A comparison of the monomial method and the S-system method for solving systems of algebraic equations
type: Item
instance of: scholarly article
title: A comparison of the monomial method and the S-system method for solving systems of algebraic equations
zbMATH Open document ID: 0907.65047
DOI: 10.1016/S0096-3003(97)00397-4
author: Scott A. Burns
author: Michael A. Savageau
author: Keith M. Mueller
published in: Applied Mathematics and Computation
publication date: 1998-08-02T00:00:00Z
review text: The computational differences between two methods (monomial method and S-system method), which are actually mathematically the same and are both equivalent to Newton's method operating on a transformed system of equations are described. It is shown that it is unclear at this time as to whether using the smaller but relatively dense monomial method linear system is more efficient than using the considerably larger, sparse linear system created using the S-system method. This paper further investigates the effectiveness of a combinatorial strategy for locating many, and sometime all, solutions to a system of nonlinear equations when applied to either of the two methods.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 1183230
zbMATH Keywords: computational efficiency
zbMATH Keywords: comparison of methods
zbMATH Keywords: monomial method
zbMATH Keywords: S-system method
zbMATH Keywords: combinatorial strategy
zbMATH Keywords: system of nonlinear equations
reviewed by: Florica Luban
describes a project that uses: ESSYNS
MaRDI profile type: Publication
cites work: The monomial method: Extensions, variations, and performance issues
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cites work: Q4003916
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full work available at URL: s0096-3003(97)00397-4
OpenAlex ID: W2028057268
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description: scientific article; zbMATH DE number 1183230