# 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