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Mathematics Research Report CMA-MRR70-94
Product Algorithms For Eigensystems
David E. Stewart
Abstract:
A number of problems arising from dynamical systems and other areas leads to
problems of computing eigenvalues/vectors and singular value decompositions
of products of matrices. A number of recent algorithms by Bojanczyk, Golub and
Van Dooren; Bojanczyk, Ewerbring and Luk; D. Stewart; and Abarbanel, Brown and
Kennel have been devised to compute Schur forms and SVD's of products in terms
of the factors. A common connection between them is the use of recursive
QR factorisations and related methods. Relationships between these methods, and
their accuracy, is discussed. Generalised eigen- and singular value
decompositions
can also be understood in this framework.
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