Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Continuation of Invariant Subspaces for Large Bifurcation Problems

David Samuel Bindel, James Demmel and Mark Friedman

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2006-13
February 13, 2006

http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-13.pdf

We summarize an algorithm for computing a smooth orthonormal basis for an invariant subspace of a parameter-dependent matrix, and describe how to extend it for numerical bifurcation analysis. We adapt the continued subspace to track behavior relevant to bifurcations, and use projection methods to deal with large problems. To test our ideas, we have integrated our code into MATCONT, a program for numerical continuation and bifurcation analysis.


BibTeX citation:

@techreport{Bindel:EECS-2006-13,
    Author = {Bindel, David Samuel and Demmel, James and Friedman, Mark},
    Title = {Continuation of Invariant Subspaces for Large Bifurcation Problems},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {2006},
    Month = {Feb},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-13.html},
    Number = {UCB/EECS-2006-13},
    Abstract = {We summarize an algorithm for computing a smooth orthonormal basis for an invariant subspace of a parameter-dependent matrix, and describe how to extend it for numerical bifurcation analysis.  We adapt the continued subspace to track behavior relevant to bifurcations, and use projection methods to deal with large problems.  To test our ideas, we have integrated our code into MATCONT, a program for numerical continuation and bifurcation analysis.}
}

EndNote citation:

%0 Report
%A Bindel, David Samuel
%A Demmel, James
%A Friedman, Mark
%T Continuation of Invariant Subspaces for Large Bifurcation Problems
%I EECS Department, University of California, Berkeley
%D 2006
%8 February 13
%@ UCB/EECS-2006-13
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-13.html
%F Bindel:EECS-2006-13