检索结果-内蒙古大学图书馆

Fast breakdown-free algorithm for computing the determinants of a generalized comrade matrix

JOURNAL OF MATHEMATICAL CHEMISTRY 2025年第5期63卷 1189-1210页

作者： Fan, Xin Jia, Ji-Teng Xidian Univ Sch Math & Stat Xian 710071 Shaanxi Peoples R China

In this paper, we consider the determinant evaluation of a generalized comrade matrix based on a novel incomplete block-diagonalization approach which transforms the determinant of the original generalized comrade matrix into the determinants of tridiagonal matrices and comrade matrix with lower-order. Then, a breakdown-free recursive algorithm for computing the determinant of the generalized comrade matrix is proposed. Even though the algorithm is not a symbolic algorithm, it never suffers from breakdown. Furthermore, we propose an explicit formula for the determinant of the generalized comrade matrix with quasi-Toeplitz structure. Some numerical results with simulations in MATLAB implementation are provided to demonstrate the accuracy and effectiveness of the proposed algorithm, and its competitiveness with MATLAB built-in function.

关键词： Comrade matrices Generalized comrade matrices Determinants Incomplete block-diagonalizations breakdown-free algorithm Tridiagonal matrices

来源：评论

学校读者我要写书评

暂无评论

A breakdown-free algorithm for computing the determinants of periodic tridiagonal matrices

引用

NUMERICAL algorithmS 2020年第1期83卷 149-163页

作者： Jia, Ji-Teng Xidian Univ Sch Math & Stat Xian 710071 Shaanxi Peoples R China

In this paper, we present a new breakdown-free recursive algorithm for computing the determinants of periodic tridiagonal matrices via a three-term recurrence. Even though the algorithm is not a symbolic algorithm, it never suffers from breakdown. Furthermore, the proposed algorithm theoretically produces exact values for periodic tridiagonal matrices whose entries are all given in integer. In addition, an explicit formula for the determinant of the periodic tridiagonal matrix with Toeplitz structure is also discussed.

关键词： Tridiagonal matrices Periodic tridiagonal matrices Determinants breakdown-free algorithm Three-term recurrence

来源：评论

学校读者我要写书评

暂无评论

A note on a fast breakdown-free algorithm for computing the determinants and the permanents of k-tridiagonal matrices

引用

APPLIED MATHEMATICS AND COMPUTATION 2014年 249卷 98-102页

作者： Sogabe, Tomohiro Yilmaz, Fatih Aichi Prefectural Univ Grad Sch Informat Sci & Technol Aichi 4801198 Japan Gazi Univ Polatli Art & Sci Fac Dept Math TR-06900 Ankara Turkey

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.

关键词： k-Tridiagonal matrix Determinant Permanent breakdown-free algorithm

来源：评论

学校读者我要写书评

暂无评论

An incomplete tridiagonalization-based determinant evaluation for a generalized periodic tridiagonal matrix

引用

NUMERICAL algorithmS 2024年 1-21页

作者： Fan, Xin Jia, Ji-Teng Xidian Univ Sch Math & Stat Xian 710071 Shaanxi Peoples R China

In this paper, we first propose a novel incomplete tridiagonalization approach for evaluating the determinant of the generalized periodic tridiagonal matrix. By the incomplete tridiagonalization approach and Laplace's theorem we transform the determinant of the generalized periodic tridiagonal matrix into the determinants of tridiagonal matrix and periodic tridiagonal matrix with lower-order. Then, we present a breakdown-free recursive algorithm for computing the determinant of the generalized periodic tridiagonal matrix based on the incomplete tridiagonalization approach. Even though the algorithm is not a symbolic algorithm, it never suffers from breakdown. Furthermore, we give an explicit formula for the determinant of the generalized periodic tridiagonal matrix with Toeplitz structure. Some numerical results with simulations in MATLAB implementation are provided to demonstrate the accuracy and effectiveness of the proposed algorithm, and its competitiveness with MATLAB built-in function.

关键词： Generalized periodic tridiagonal matrices Determinants Incomplete tridiagonalizations breakdown-free algorithm Tridiagonal matrices Periodic tridiagonal matrices

来源：评论

学校读者我要写书评

暂无评论

An incomplete block-diagonalization approach for evaluating the determinants of bordered k-tridiagonal matrices

引用

JOURNAL OF MATHEMATICAL CHEMISTRY 2022年第8期60卷 1658-1673页

作者： Jia, Ji-Teng Wang, Jie Yuan, Ting-Feng Zhang, Kai-Kai Zhong, Bao-Ming Xidian Univ Sch Math & Stat Xian 710071 Peoples R China

In this paper, we present an efficient numerical algorithm for evaluating the determinants of general bordered k-tridiagonal matrices in linear time. The algorithm is based on a novel incomplete block-diagonalization (IBD) approach which preserves the low-rank structure and sparsity of the original matrix, and a reliable algorithm for the determinants of general bordered tridiagonal matrices. An advantage of the proposed algorithm is that there is no division operation involved and hence the algorithm will never suffer from breakdown. Moreover, the algorithm theoretically produces exact values of the determinants when all entries of the bordered k-tridiagonal matrix are given in integer. Some numerical results with simulations in Matlab implementation are provided in order to illustrate the accuracy and effectiveness of the proposed algorithm, and its competitiveness with Gaussian elimination algorithm and MATLAB built-in function.

关键词： Bordered tridiagonal matrices k-Tridiagonal matrices Determinants Block-diagonalizations breakdown-free algorithm

来源：评论

学校读者我要写书评

暂无评论

Numerical algorithms for the determinants of opposite-bordered and singly-bordered tridiagonal matrices

引用

JOURNAL OF MATHEMATICAL CHEMISTRY 2020年第9期58卷 1828-1845页

作者： Jia, Ji-Teng Xidian Univ Sch Math & Stat Xian 710071 Shaanxi Peoples R China

A recursive algorithm for the determinant evaluation of general opposite-bordered tridiagonal matrices has been proposed by Jia et al. (J Comput Appl Math 290:423-432, 2015). Since the algorithm is a symbolic algorithm, it never suffers from breakdown. However, it may be time-consuming when many symbolic names emerge during the symbolic computation. In this paper, without using symbolic computation, first we present a novel breakdown-free numerical algorithm for computing the determinant of ann-by-nopposite-bordered tridiagonal matrix, which does not require any extra memory storage for the implementation. Then, we present a cost-efficient algorithm for the determinants of opposite-bordered tridiagonal matrices based on the use of the combination of an elementary column operation and Sylvester's determinant identity. Furthermore, we provide some numerical results with simulations in Matlab implementation in order to demonstrate the accuracy and efficiency of the proposed algorithms, and their competitiveness with other existing algorithms. The corresponding results in this paper can be readily obtained for computing the determinants of singly-bordered tridiagonal matrices.

关键词： Opposite-bordered tridiagonal matrices Singly-bordered tridiagonal matrices Determinants breakdown-free algorithm Cost-efficient algorithm

来源：评论

学校读者我要写书评

暂无评论

Numerical algorithms for the determinant evaluation of general Hessenberg matrices

引用

JOURNAL OF MATHEMATICAL CHEMISTRY 2018年第1期56卷 247-256页

作者： Jia, Ji-Teng Xidian Univ Sch Math & Stat Xian 710071 Shaanxi Peoples R China

Hessenberg matrices frequently arise in many application areas and have been attracted much attention in recent years. In the current paper, we present two numerical algorithms of for computing the determinant of an n-by-n general Hessenberg matrix. The algorithms are all suited for implementation using Computer Algebra Systems such as MATLAB and MAPLE. Some numerical examples are provided in order to demonstrate the performance of the proposed algorithms.

关键词： Hessenberg matrices Determinants breakdown-free algorithm Two-term recurrence Computational cost

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：