Actions of noncompact groups and algorithm design: A case study

Klaus Diepold, Rainer Pauli

Research output: Contribution to journalConference articlepeer-review


Numerical matrix computations involving actions of non-compact transformation groups are known to produce numerical problems since the elements of the pertaining matrix representations are inherently unbounded. In this case study we analyze numerical problems occurring in a class of algorithms that is based on actions of the pseudo-orthogonal group On,m - a group that is noncompact (hyperbolic geometry) and well established in signal processing (Schur methods). As a major result, it is shown how to exploit the additional degrees of freedom in defining coordinate frames in a Grassmannian setting in order to impose an a priori bound on the norm of the transformation matrices. This way, numerically disastrous situations can be circumvented systematically. Hence, it becomes possible to develop modified algorithms which exhibit superior numerical performance for a large class of problems based on e.g. hyperbolic transformations.

Original languageEnglish
Pages (from-to)47-50
Number of pages4
JournalICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
StatePublished - 1997
Externally publishedYes
EventProceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP. Part 1 (of 5) - Munich, Ger
Duration: 21 Apr 199724 Apr 1997


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