A fast numerical algorithm for the determinant of a pentadiagonal matrix

• Published in: Applied mathematics and computation Vol. 196; no. 2; pp. 835 - 841
• Main Author: Sogabe, Tomohiro
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01-03-2008; Elsevier
• Subjects: Determinants; Exact sciences and technology; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Pentadiagonal matrices; Quindiagonal matrices; Sciences and techniques of general use; Quindiagonal matrices; Determinants; Pentadiagonal matrices; Numerical analysis; Applied mathematics; Recurrence relation; Determinant; Fast algorithm; Tridiagonal matrix
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2007.07.015

Recently, a two-term recurrence for the determinant of a general matrix has been found [T. Sogabe, On a two-term recurrence for the determinant of a general matrix, Appl. Math. Comput., 187 (2007) 785–788] and it leads to a natural generalization of the DETGTRI algorithm [M. El-Mikkawy, A fast algorithm for evaluating
nth order tridiagonal determinants, J. Comput. Appl. Math. 166 (2004) 581–584] for computing the determinant of a tridiagonal matrix. In this paper, we derive a fast numerical algorithm for computing the determinant of a pentadiagonal matrix from the generalization of the DETGTRI algorithm.