Document Type
Article
Publication Date
2009
Keywords
Separable parameterized equations, static bifurcation points, extended systems, Newton's method, LU factorization, curve switching and tracking
Abstract
Many applications give rise to separable parameterized equations, which have the form A(y, µ)z + b(y, µ) = 0, where z ∈ RN , y ∈ Rn, µ ∈ Rs, and the (N + n) × N matrix A(y, µ) and (N + n) vector b(y, µ) are C2 -Lipschitzian in (y, µ) ∈ Ω ⊂ Rn × Rs. We present a technique which reduces the original equation to the form f (y, µ) = 0, where f : Ω → Rn is C2 -Lipschitzian in (y, µ). This reduces the dimension of the space within which the bifurcation relation occurs. We derive expressions required to implement methods to solve the reduced equation. Numerical examples illustrate the use of the technique.
Publication Title
Electronic Transactions on Numerical Analysis
Volume
34
First Page
31
Last Page
43
Required Publisher's Statement
Copyright 2009, Kent State University. ISSN 1068-9613
Recommended Citation
Shen, Yun-Qiu and Ypma, Tjalling, "Numerical Bifurcation of Separable Parameterized Equations" (2009). Mathematics Faculty Publications. 91.
https://cedar.wwu.edu/math_facpubs/91
Subjects - Topical (LCSH)
Singular value decomposition; Separable algebras; Bifurcation theory; Differential equations, Nonlinear; Newton-Raphson method
Genre/Form
articles
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Language
English
Format
application/pdf
