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Towards a more robust algorithm for computing the restricted singular value decomposition
Ian N. Zwaan
A new algorithm to compute the restricted singular value decomposition of dense matrices is presented. Like Zha's method \cite{Zha92}, the new algorithm uses an implicit Kogbetlian…
Krylov type methods exploiting the quadratic numerical range
Andreas Frommer, Birgit Jacob, Karsten Kahl +2
The quadratic numerical range is a subset of the standard numerical range of a linear operator which still contains its spectrum. It arises naturally in operators which ha…
Cross product-free matrix pencils for computing generalized singular values
Ian N. Zwaan
It is well known that the generalized (or quotient) singular values of a matrix pair can be obtained from the generalized eigenvalues of a matrix pencil consisting of two…
Generalized Davidson and multidirectional-type methods for the generalized singular value decomposition
Ian N. Zwaan, Michiel E. Hochstenbach
We propose new iterative methods for computing nontrivial extremal generalized singular values and vectors. The first method is a generalized Davidson-type algorithm and the second…