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Accurate computation of eigenvalues of generalized sign regular quasi-Said–Ball–Vandermonde matrices

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Abstract

In this paper, a class of quasi-Said-Ball-Vandermonde (q-SBV) matrices belonging to generalized sign regular matrices with signature \((1,\dots ,1,-1)\) is introduced. We first accurately compute all the parameters of q-SBV matrices from their bidiagonal decompositions. Furthermore, an algorithm is proposed for computing all the eigenvalues of q-SBV matrices to high relative accuracy by using the accurate parameters. At last, some numerical experiments are presented to show the efficiency and accuracy of our algorithms.

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Acknowledgements

The author is thankful to the editors and the anonymous referees for their valuable comments to improve the paper.

Funding

The work was supported by the Scientific Research Project of Education Department of Hunan Province (Grant No. 21C0837).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Hunan First Normal University, Changsha, 410205, Hunan, People’s Republic of China

    Yebo Xiong

  2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Yebo Xiong

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Xiong, Y. Accurate computation of eigenvalues of generalized sign regular quasi-Said–Ball–Vandermonde matrices. Calcolo 60, 39 (2023). https://doi.org/10.1007/s10092-023-00534-4

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  • DOI: https://doi.org/10.1007/s10092-023-00534-4

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