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, vol.249, pp.98-102, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 249
  • Publication Date: 2014
  • Doi Number: 10.1016/j.amc.2014.10.040
  • Title of Journal : APPLIED MATHEMATICS AND COMPUTATION
  • Page Numbers: pp.98-102
  • Keywords: k-Tridiagonal matrix, Determinant, Permanent, Breakdown-free algorithm, INVERSES

Abstract

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.