检索结果-南通市图书馆

A Novel Iterative Method to Find the Moore-Penrose Inverse of a Tensor with Einstein Product

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS 2024年第1期17卷 37-68页

作者： Erfanifar, Raziyeh Hajarian, Masoud Sayevand, Khosro Shahid Beheshti univ Fac Math Sci Dept Appl Math Tehran Iran malayer univ Fac Math & Stat Malayer Iran

In this study, based on an iterative method to solve nonlinear equations, a third-order convergent iterative method to compute the Moore-Penrose inverse of a tensor with the Einstein product is presented and analyzed. Numerical comparisons of the proposed method with other methods show that the average number of iterations, number of the Einstein products, and CPU time of our method are considerably less than other methods. In some applications, partial and fractional differential equations that lead to sparse matrices are considered as prototypes. We use the iterates obtained by the method as a preconditioner, based on tensor form to solve the multilinear system A *N X = 13. Finally, several practical numerical examples are also given to display the accuracy and efficiency of the new method. The presented results show that the proposed method is very robust for obtaining the Moore-Penrose inverse of tensors.

关键词： Tensor iterative methods Moore-Penrose inverse Einstein product ORDER TENSOR DIFFUSION

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

On Polar Decomposition of Tensors with Einstein Product and a Novel Iterative Parametric Method

引用

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS 2024年第1期17卷 69-92页

作者： Erfanifar, Raziyeh Hajarian, Masoud Sayevand, Khosro Shahid Beheshti univ Fac Math Sci Dept Appl Math Tehran Iran malayer univ Fac Math & Stat Malayer Iran

This study aims to investigate the polar decomposition of tensors with the Einstein product for the first time. The polar decomposition of tensors can be computed using the singular value decomposition of the tensors with the Einstein product. In the following, some iterative methods for finding the polar decomposi-tion of matrices have been developed into iterative methods to compute the polar decomposition of tensors. Then, we propose a novel parametric iterative method to find the polar decomposition of tensors. Under the obtained conditions, we prove that the proposed parametric method has the order of convergence four. In every iteration of the proposed method, only four Einstein products are required, while other iterative methods need to calculate multiple Einstein products and one tensor inversion in each iteration. Thus, the new method is superior in terms of efficiency index. Finally, the numerical comparisons performed among several well-known methods, show that the proposed method is remarkably efficient and accurate.

关键词： Iterative methods Einstein product polar decomposition of a tensor polar factor order of convergence ALGORITHMS MATRIX

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

欢迎您,

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

在线全文

在线全文

请选择保存的检索档案：

请选择收藏分类：

通借通还

欢迎您,

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

在线全文

在线全文

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：