• Corpus ID: 209404986

Cross product-free matrix pencils for computing generalized singular values

@article{Zwaan2019CrossPM,
  title={Cross product-free matrix pencils for computing generalized singular values},
  author={Ian N. Zwaan},
  journal={ArXiv},
  year={2019},
  volume={abs/1912.08518}
}
  • I. Zwaan
  • Published 18 December 2019
  • Mathematics
  • ArXiv
It is well known that the generalized (or quotient) singular values of a matrix pair $(A, C)$ can be obtained from the generalized eigenvalues of a matrix pencil consisting of two augmented matrices. The downside of this reformulation is that one of the augmented matrices requires a cross products of the form $C^*C$, which may affect the accuracy of the computed quotient singular values if $C$ has a large condition number. A similar statement holds for the restricted singular values of a matrix… 

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