# 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} }

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…

## 2 Citations

Two harmonic Jacobi-Davidson methods for computing a partial generalized singular value decomposition of a large matrix pair

- Computer ScienceArXiv
- 2022

Two harmonic extraction based Jacobi–Davidson (JD) type algorithms are proposed to compute a partial generalized singular value decomposition (GSVD) of a large regular matrix pair and converge more regularly and suit better for computing GSVD components corresponding to interior generalized singular values.

Some applications of a decomposition for five quaternion matrices in control system and color image processing

- MathematicsComput. Appl. Math.
- 2021

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