Computation of Bifurcation Graphs.
Please always quote using this URN: urn:nbn:de:0297-zib-837
- 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.
| Author: | Karin Gatermann |
|---|---|
| Document Type: | ZIB-Report |
| Date of first Publication: | 1992/05/21 |
| Series (Serial Number): | ZIB-Report (SC-92-13) |
| ZIB-Reportnumber: | SC-92-13 |
| Published in: | 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 |
