An algebraic geometric method to calculate branches near a bifurcation point
type: Item
instance of: scholarly article
title: An algebraic geometric method to calculate branches near a bifurcation point
zbMATH Open document ID: 0706.65046
DOI: 10.1016/0898-1221(90)90360-V
author: U. Jin Choi
author: Sung H. Bae
author: Do Y. Kwak
publication date: 1990-01-01T00:00:00Z
review text: Although not explicitly stated in the introduction, the paper deals only with systems of polynomial equations \(F(x)=0,\quad F: {\mathbb{R}}^{n+1}\to {\mathbb{R}}^ n.\) In particular, the problem is studied how to calculate solution branches near a bifurcation point. The algebraic geometric concept of ``blowing up'' is utilized to regularize the Jacobian at the bifurcation point. Then the different branches are calculated by a standard continuation method. The original branches are obtained by ``blowing them down''. The method is illustrated for a simple example.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65H20
zbMATH DE Number: 4159981
zbMATH Keywords: algebraic geometric method
zbMATH Keywords: systems of polynomial equations
zbMATH Keywords: solution branches
zbMATH Keywords: bifurcation point
zbMATH Keywords: blowing up
zbMATH Keywords: continuation method
reviewed by: Walter Zulehner
MaRDI profile type: Publication
cites work: Path following near bifurcation
cites work: Efficient Numerical Pathfollowing Beyond Critical Points
cites work: Q5571530
cites work: Characterization and Computation of Generalized Turning Points
cites work: Q4143433
cites work: Quadratically Convergent Methods for the Computation of Unfolded Singularities
cites work: Q3723608
cites work: Characterization and Computation of Singular Points with Maximum Rank Deficiency
cites work: Some computational aspects of the stability analysis of nonlinear structures
cites work: Numerical Methods for a Class of Finite Dimensional Bifurcation Problems
cites work: Solution Fields of Nonlinear Equations and Continuation Methods
full work available at URL: 0898-1221(90)90360-v
OpenAlex ID: W2019590545
published in: Computers & Mathematics with Applications
Recommended article: Q4872663
Recommended article: Geometric description and computational method for bifurcation
Recommended article: Q4214180
Recommended article: Q3991275
Recommended article: Q3744924
Recommended article: Numerical approximations of solution branches of a bifurcation point
Recommended article: A numerical method for branch points of a system of nonlinear algebraic equations
Recommended article: Q3982289
Recommended article: Q3344087
Recommended article: Q3696083
description: scientific article; zbMATH DE number 4159981