An elementary algorithm for computing the determinant of pentadiagonal Toeplitz matrices
type: Item
instance of: scholarly article
title: An elementary algorithm for computing the determinant of pentadiagonal Toeplitz matrices
zbMATH Open document ID: 1254.65059
published in: Journal of Computational and Applied Mathematics
publication date: 2012-03-19T00:00:00Z
review text: The author presents a new kind of elementary algorithm for computing the determinants of pentadiagonal Toeplitz matrices of order \(n\). This algorithm requires \(56\dot\lfloor\frac{n-4}k\rfloor+30k+O(\log n)\) operations, where \(k\geq 4\) is an integer chosen freely at the beginning of the algorithm. Another main result of this paper gives a fast algorithm for determining when the determinants of pentadiagonal Toeplitz matrices with rational entries are nonzero.
Mathematics Subject Classification ID: 65F40
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 6015745
zbMATH Keywords: pentadiagonal matrix
zbMATH Keywords: Toeplitz matrix
zbMATH Keywords: determinant
zbMATH Keywords: fast algorithm
author: Zübeyir Çınkır
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: j.cam.2011.11.017
OpenAlex ID: W2023158837
cites work: A computational algorithm for special \(n\)th-order pentadiagonal Toeplitz determinants
cites work: A general 4th-order PDE method to generate Bézier surfaces from the boundary
cites work: A recursive relation for the determinant of a pentadiagonal matrix
cites work: A recursive algorithm for determining the eigenvalues of a quindiagonal matrix
cites work: On the eigenvalue problem for Toeplitz band matrices
cites work: Efficient Algorithms for the Evaluation of the Eigenvalues of (Block) Banded Toeplitz Matrices
cites work: A fast numerical algorithm for the determinant of a pentadiagonal matrix
cites work: A note on computing the inverse and the determinant of a pentadiagonal Toeplitz matrix
cites work: A fast elementary algorithm for computing the determinant of Toeplitz matrices
cites work: A fast algorithm for solving diagonally dominant symmetric pentadiagonal Toeplitz systems
DOI: 10.1016/J.CAM.2011.11.017
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description: scientific article; zbMATH DE number 6015745