A power series method for computing singular solutions to nonlinear analytic systems
type: Item
instance of: scholarly article
title: A power series method for computing singular solutions to nonlinear analytic systems
zbMATH Open document ID: 0756.65079
DOI: 10.1007/BF01385867
author: Alexander P. Morgan
author: Charles W. Wampler
author: Andrew J. Sommese
published in: Numerische Mathematik
publication date: 1993-02-02T00:00:00Z
full work available at URL: https://eudml.org/doc/133687
review text: Given a system of analytic equations having a singular solution, we show how to develop a power series representation for the solution. This series is computable, and when the multiplicity of the solution is small, highly accurate estimates of the solution can be generated for a moderate computational cost. In this paper, a theorem is proven (using results from several complex variables) which establishes the basis for the approach. Then a specific numerical method is developed, and data from numerical experiments are given.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 65H20
zbMATH DE Number: 86137
zbMATH Keywords: continuation method
zbMATH Keywords: holomorphic system
zbMATH Keywords: homotopy method
zbMATH Keywords: nonlinear system
zbMATH Keywords: polynomial system
zbMATH Keywords: root
zbMATH Keywords: zero
zbMATH Keywords: system of analytic equations
zbMATH Keywords: singular solution
zbMATH Keywords: power series representation
zbMATH Keywords: several complex variables
describes a project that uses: PITCON
describes a project that uses: HOMPACK
MaRDI profile type: Publication
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OpenAlex ID: W2093101196
description: scientific article; zbMATH DE number 86137