Abstract
In this paper, we propose a new structure-preserving algorithm for computing the singular value decomposition of a quaternion matrix A. We first prove that the multiplication of two complex adjoint matrices will still be a complex adjoint matrix. Thus, utilizing this fact, we conduct a sequence of unitary complex adjoint matrices on a half of the elements of the complex adjoint matrix \(\chi _A\) of A instead of the whole \(\chi _A\). Then, we recover the resulting matrix with the help of the special structures. This method also reveals an efficient way to preserve some specific structures implicitly. Moreover, comparing with other algorithms, the numerical experiments show that our algorithm has higher accuracy when computing the QSVD of a large scale quaternion matrix.
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Acknowledgements
The authors would like to thank Prof. Zhigang Jia’s help and the anonymous referees for their valuable comments and suggestions.
Funding
This research is supported by Macao Science and Technology Development Fund (No. 0013/2021/ITP), the grants from the National Natural Science Foundation of China (12371023, 12271338), and the Natural Sciences and Engineering Research Council of Canada (NSERC) (RGPIN 2020-06746), The Joint Research and Development Fund of Wuyi University, Hong Kong and Macao (2019WGALH20), Macau University of Science and Technology Faculty Research Grants (FRG-22-073-FIE).
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Yu, CE., Liu, X. & Zhang, Y. A New Complex Structure-Preserving Method for QSVD. J Sci Comput 99, 37 (2024). https://doi.org/10.1007/s10915-024-02496-3
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DOI: https://doi.org/10.1007/s10915-024-02496-3