Construction of iteration functions for the simultaneous computation of the solutions of equations and algebraic systems
type: Item
instance of: scholarly article
title: Construction of iteration functions for the simultaneous computation of the solutions of equations and algebraic systems
zbMATH Open document ID: 0804.65053
DOI: 10.1007/BF02142677
author: Anne-Mercedes Bellido
published in: Numerical Algorithms
publication date: 1995-01-15T00:00:00Z
review text: The author constructs Newton-like iteration methods for the real solutions of systems of algebraic equations. The methods considered are related to and generalize the methods of Durand and Kerner for the calculation of all real roots of univariate polynomials via, e.g., the symmetric equations for the roots of a polynomial. Analogous resolvent systems are formulated and the iteration maps for such systems are simplified Newton maps. Local quadratic convergence results are given. Several numerical examples are also given. It would be of interest to compare the performance of the present method with the recently developed homotopy continuation methods for this class of problems.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 12Y05
zbMATH DE Number: 553668
zbMATH Keywords: local quadratic convergence
zbMATH Keywords: Durand-Kerner method
zbMATH Keywords: Newton-like iteration methods
zbMATH Keywords: systems of algebraic equations
zbMATH Keywords: numerical examples
zbMATH Keywords: performance
reviewed by: Eugene L. Allgower
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 553668