Improved detection of bifurcations in large nonlinear systems via the continuation of invariant subspaces algorithm

The Continuation of Invariant Subspaces (CIS) algorithm [Demmel et al., 200 1; Dieci & Friedman, 2001] produces a smooth orthogonal similarity transfor mation to block triangular form of a parameter dependent matrix A(s). The C IS algorithm is an adaptation of an iterative refinement technique for impr oving the accuracy of computed invariant subspaces. On the basis of the CIS algorithm, new test functions are defined for an im proved, more reliable detection of bifurcations in problems with simple bif urcations near multiple bifurcations, problems with multiple bifurcations, and problems with symmetries. Illustrative examples are given.