A note on a fast breakdown-free algorithm for computing the determinants and the permanents of k-tridiagonal matrices

Sogabe T., YILMAZ F.

APPLIED MATHEMATICS AND COMPUTATION, cilt.249, ss.98-102, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 249
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1016/j.amc.2014.10.040
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.98-102
  • Anahtar Kelimeler: k-Tridiagonal matrix, Determinant, Permanent, Breakdown-free algorithm, INVERSES
  • Ankara Hacı Bayram Veli Üniversitesi Adresli: Hayır

Özet

k-Tridiagonal matrices have attracted much attention in recent years, which are a generalization of tridiagonal matrices. In this note, a breakdown-free numerical algorithm of O(n) is presented for computing the determinants and the permanents of k-tridiagonal matrices. Even though the algorithm is not a symbolic algorithm, it never suffers from breakdown. Furthermore, it produces exact values when all entries of the k-tridiagonal matrices are given in integer. In addition, the algorithm can be simplified for a general symmetric Toeplitz case, and it generates the kth powers of Fibonacci, Pell, and Jacobsthal numbers for a certain symmetric Toeplitz case. (C) 2014 Elsevier Inc. All rights reserved.