Continuation of Invariant Subspaces for Large and Sparse bifurcations problems.
by
Mark Friedman
Mathematical Sciences Department University of Alabama in Huntsville
Coauthors: David Bindel (Computer Science Division, University of California, Berkeley), James Demmel (Computer Science Division and Department of Mathematics, University of California, Berkeley), Mark Jackson (NASA/Marshall Space Flight Center, Huntsville, Alabama)

The Continuation of Invariant Subspaces (CIS) algorithm [Demmel, Dieci, Friedman 2001] and [Dieci, Friedman 2000], produces a smoothly varying basis for an invariant subspace R(s) of a parameter dependent matrix A(s).

We consider the situation when the continued spectral set, associated with R(s), corresponds to few eigenvalues of A(s) near the imaginary axis and contains all information about potential bifurcations.

We develop reliable procedures for updating R(s) when eigenvalues are added and/or removed from the continued spectral set.

We extend the CIS algorithm to the case of large sparse matrices using projection methods.

We consider several examples, including stability analysis of a simulation model of the single stage to orbit reusable launch vehicle called the X-33.

Date received: February 26, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakr-64.