Yun-Qiu Shen, Tjalling J. Ypma
Abstract:
Many applications give rise to separable parameterized equations
of the form
, where
,
and the parameter
;
here
is an
matrix and
.
Under the assumption that
has full rank we showed in [21] that
bifurcation points can be located by solving a reduced equation
of the form
.
In this paper we extend that method
to the case that
has rank deficiency one at the
bifurcation point. At such a point the solution curve
branches into infinitely many additional solutions, which form
a straight line. A numerical method for reducing the problem to a
smaller space and locating such a bifurcation point is given.
Applications to equilibrium solutions of nonlinear ordinary
equations and solutions of discretized partial differential
equations are provided.
Published September 25, 2010.
Math Subject Classifications: 65P30, 65H10, 34C23, 37G10.
Key Words: Separable parameterized equations; bifurcation; rank deficiency;
Golub-Pereyra variable projection method; bordered matrix;
singular value decomposition; Newton's method.
Show me the PDF file (248K), TEX file, and other files for this article.
Yun-Qiu Shen Department of Mathematics, Western Washington University Bellingham, WA 98225-9063, USA email: yunqiu.shen@wwu.edu | |
Tjalling J. Ypma Department of Mathematics, Western Washington University Bellingham, WA 98225-9063, USA email: tjalling.ypma@wwu.edu |
Return to the table of contents
for this conference.
Return to the EJDE web page