A fast elementary algorithm for computing the determinant of Toeplitz matrices


Cinkir Z.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.255, ss.353-361, 2014 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 255
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1016/j.cam.2013.05.014
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Sayfa Sayısı: ss.353-361

Özet

In recent years, a number of fast algorithms for computing the determinant of a Toeplitz matrix were developed. The fastest algorithm we know so far is of order k(2) log n + k(3), where n is the number of rows of the Toeplitz matrix and k is the bandwidth size. This is possible because such a determinant can be expressed as the determinant of certain parts of the n-th power of a related k x k companion matrix. In this paper, we give a new elementary proof of this fact, and provide various examples. We give symbolic formulas for the determinants of Toeplitz matrices in terms of the eigenvalues of the corresponding companion matrices when k is small. (C) 2013 Elsevier B.V. All rights reserved.