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Computing the Determinant of a Matrix with Polynomial Entries by Approximation

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Abstract

Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. This paper proposes an effective algorithm to compute the determinant of a matrix with polynomial entries using hybrid symbolic and numerical computation. The algorithm relies on the Newton’s interpolation method with error control for solving Vandermonde systems. The authors also present the degree matrix to estimate the degree of variables in a matrix with polynomial entries, and the degree homomorphism method for dimension reduction. Furthermore, the parallelization of the method arises naturally.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, 610064, China

    Xiaolin Qin

  2. Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu, 610041, China

    Xiaolin Qin, Zhi Sun & Yong Feng

  3. School of Computer Engineering and Science, Shanghai University, Shanghai, 200444, China

    Tuo Leng

Authors
  1. Xiaolin Qin
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  2. Zhi Sun
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  3. Tuo Leng
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  4. Yong Feng
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Corresponding author

Correspondence to Xiaolin Qin.

Additional information

This research was supported by China 973 Project under Grant No. 2011CB302402, the National Natural Science Foundation of China under Grant Nos. 61402537, 11671377, 91118001, and China Postdoctoral Science Foundation funded project under Grant No. 2012M521692.

This paper was recommended for publication by Editor-in-Chief GAO Xiao-Shan.

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Qin, X., Sun, Z., Leng, T. et al. Computing the Determinant of a Matrix with Polynomial Entries by Approximation. J Syst Sci Complex 31, 508–526 (2018). https://doi.org/10.1007/s11424-017-6033-8

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  • DOI: https://doi.org/10.1007/s11424-017-6033-8

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