In recent years, a number of numerical algorithms of O(n) for computing the determinants of cyclic pentadiagonal matrices have been developed. In this paper, a cost-efficient numerical algorithm for the determinant of an n-by-n cyclic pentadiagonal Toeplitz matrix is proposed whose computational cost is estimated at O(logn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\log n)$$\end{document}. The algorithm is based on a structure-preserving matrix factorization and a three-term recurrence relation. We provide some numerical results with simulations in Matlab implementation in order to demonstrate the accuracy and effectiveness of the proposed algorithm, and its competitiveness with other existing algorithms.

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关于循环五对角 Toeplitz 矩阵行列式的保结构矩阵分解

近年来，已经开发了许多用于计算循环五对角矩阵行列式的 O(n) 数值算法。在本文中，提出了一种用于 n×n 循环五对角 Toeplitz 矩阵行列式的经济高效的数值算法，其计算成本估计为 O(logn)\documentclass[12pt]{minimal}\usepackage{amsmath}\ usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\log n)$$\end{文档}。该算法基于保留结构的矩阵分解和三项递推关系。我们提供了一些数值结果，并在 Matlab 实现中进行了模拟，以证明所提出算法的准确性和有效性，