Continuation of Invariant Subspaces in Large Bifurcation Problems
David Bindel, James Weldon Demmel, Mark Jay Friedman · SIAM Journal on Scientific Computing · 2008
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.