Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 30, Issue 2, Pages 637-656Publisher
SIAM PUBLICATIONS
DOI: 10.1137/060654219
Keywords
smooth eigendecompositions; invariant subspaces; continuation; bifurcation analysis; Ritz-Galerkin methods
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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.
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