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A Note on the Square Roots of a Class of Circulant Matrices

Author

Listed:
  • Ying Zhang
  • Huisheng Zhang
  • Guoyan Chen

Abstract

We prove that any k‐circulant matrix and any even order skew k‐circulant matrix are diagonalizable for any k ∈ ℂ. Then, we propose two algorithms for computing the square roots of the k‐circulant matrix and the skew k‐circulant matrix, respectively. In particular, we show that the square roots of the k‐circulant matrix are still k‐circulant matrices. Both the theoretical analysis and the numerical experiments show that our algorithms are faster than the standard Schur method.

Suggested Citation

  • Ying Zhang & Huisheng Zhang & Guoyan Chen, 2013. "A Note on the Square Roots of a Class of Circulant Matrices," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:601243
    DOI: 10.1155/2013/601243
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    References listed on IDEAS

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    1. Ying Mei, 2012. "Computing the Square Roots of a Class of Circulant Matrices," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, November.
    2. Ying Mei, 2012. "Computing the Square Roots of a Class of Circulant Matrices," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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