Computation of Bifurcation Graphs.
An abbreviated vers. appeared in: E. Allgower, K. Goerg, R. Miranda (eds.), Exploiting Symmetry in Applied and Numerical Analysis, AMS Lectures in Applied Mathematics, 1993
| SC 92-13 | Karin Gatermann
Computation of Bifurcation Graphs. An abbreviated vers. appeared in: E. Allgower, K. Goerg, R. Miranda (eds.), Exploiting Symmetry in Applied and Numerical Analysis, AMS Lectures in Applied Mathematics, 1993 | |
Abstract: The numerical treatment of Equivariant
parameter-dependent onlinear equation systems, and even more
its automation requires the intensive use of group theory.
This paper illustrates the group theoretic computations
which are done in the preparation of the numerical
computations. The bifurcation graph which gives the
bifurcation subgroups is determined from the
interrelationship of the irreducible representations of a
group and its subgroups. The Jacobian is transformed to
block diagonal structure using a modification of the
transformation which transforms to block diagonal structure
with respect to a supergroup. The principle of conjugacy is
used everywhere to make symbolic and numerical computations
even more efficient. Finally, when the symmetry reduced
problems and blocks of Jacobian matrices are evaluated
numerically, the fact that the given representation is a
quasi-permutation representation is exploited automatically.