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On choices of formulations of computing the generalized singular value decomposition of a large matrix pair

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Abstract

For the computation of the generalized singular value decomposition (GSVD) of a large matrix pair (A,B) of full column rank, the GSVD is commonly formulated as two mathematically equivalent generalized eigenvalue problems, so that a generalized eigensolver can be applied to one of them and the desired GSVD components are then recovered from the computed generalized eigenpairs. Our concern in this paper is, in finite precision arithmetic, which generalized eigenvalue formulation is numerically preferable to compute the desired GSVD components more accurately. We make a detailed perturbation analysis on the two formulations and show how to make a suitable choice between them. Numerical experiments illustrate the results obtained.

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Acknowledgments

We would like to thank the two referees very much for their valuable suggestions and comments, which made us to improve on the paper presentation.

Funding

This study was supported by the National Natural Science Foundation of China (No.11771249).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Jinzhi Huang & Zhongxiao Jia

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  1. Jinzhi Huang
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  2. Zhongxiao Jia
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Correspondence to Zhongxiao Jia.

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Huang, J., Jia, Z. On choices of formulations of computing the generalized singular value decomposition of a large matrix pair. Numer Algor 87, 689–718 (2021). https://doi.org/10.1007/s11075-020-00984-9

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  • DOI: https://doi.org/10.1007/s11075-020-00984-9

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