A note on a fast breakdown-free algorithm for computing the determinants and the permanents of k-tridiagonal matrices
APPLIED MATHEMATICS AND COMPUTATION, cilt.249, ss.98-102, 2014 (SCI-Expanded, Scopus)
- 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.