On the Computation of the Restricted Singular Value Decomposition via the Cosine-Sine Decomposition

@article{Chu2000OnTC,
  title={On the Computation of the Restricted Singular Value Decomposition via the Cosine-Sine Decomposition},
  author={Delin Chu and Lieven De Lathauwer and Bart De Moor},
  journal={SIAM J. Matrix Analysis Applications},
  year={2000},
  volume={22},
  pages={580-601}
}
In this paper, we show that the restricted singular value decomposition of a matrix triplet $A\in \R^{n \times m}, B\in \R^{n \times l}, C\in \R^{p \times m}$ can be computed by means of the cosine-sine decomposition. In the first step, the matrices A, B, C are reduced to a lower-dimensional matrix triplet ${\cal A}, {\cal B}, {\cal C}$, in which ${\cal B}$ and ${\cal C}$ are nonsingular, using orthogonal transformations such as the QR-factorization with column pivoting and the URV… CONTINUE READING

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