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A Periodic qd-Type Reduction for Computing Eigenvalues of Structured Matrix Products to High Relative Accuracy

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Abstract

In this paper, we consider the product eigenvalue problem for a wide class of structured matrices containing the well-known Vandermonde and Cauchy matrices. A periodic qd-type reduction method is developed for computing eigenvalues of products of these rectangular matrices so that no subtraction of like-signed numbers occurs. Consequently, all the eigenvalues of such a product are computed to high relative accuracy in a preferable complexity. Error analysis and numerical experiments are provided to confirm the high relative accuracy.

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Acknowledgements

The author would like to thank the Associate Editor and the anonymous referees for their valuable comments and suggestions which have helped to improve the overall presentation of the paper.

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, China

    Rong Huang

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  1. Rong Huang
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Correspondence to Rong Huang.

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Research supported by the National Natural Science Foundation of China (Grant No. 11471279), the Natural Science Foundation for Distinguished Young Scholars of Hunan Province (Grant No. 2017JJ1025) and the Research Foundation of Education Bureau of Hunan Province (Grant No. 14B178).

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Huang, R. A Periodic qd-Type Reduction for Computing Eigenvalues of Structured Matrix Products to High Relative Accuracy. J Sci Comput 75, 1229–1261 (2018). https://doi.org/10.1007/s10915-017-0584-7

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  • DOI: https://doi.org/10.1007/s10915-017-0584-7

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