Iterative methods for solving tensor equations based on exponential acceleration

doi:10.1007/s11075-023-01692-w

	Iterative methods for solving tensor equations based on exponential acceleration
	Liang, Maolin 1; Dai, Lifang 1; Zhao, Ruijuan2
	2023-11-13
发表期刊	NUMERICAL ALGORITHMS
摘要	The tensor equation Ax(m-1) = b with the tensor A of order m and dimension n and the vector b, has practical applications in several fields including signal processing, high dimensional PDEs, high-order statistics, and so on. In this paper, a class of exponential accelerated iterative methods is proposed for solving the tensor equation mentioned above in the sense that the coefficient tensor A is a symmetric and nonsingular or singular M-tensor. The obtained iterative schemes involve the classical Newton's method as a special case. It is shown that the proposed method for nonsingular case is superlinearly convergent, while for singular cases, it is linearly convergent. The performed numerical experiments demonstrate that our methods outperform some existing ones.
关键词	Tensor equations Symmetric M-tensors Newton method Exponential acceleration
DOI	10.1007/s11075-023-01692-w
收录类别	SCIE
ISSN	1017-1398
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:001103816200001
出版者	SPRINGER
原始文献类型	Article ; Early Access
EISSN	1572-9265
引用统计	被引频次[WOS]：0 [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.lzufe.edu.cn/handle/39EH0E1M/35473
专题	信息工程与人工智能学院
通讯作者	Liang, Maolin
作者单位	1.Tianshui Normal Univ, Sch Math & Stat, Tianshui 741001, Peoples R China; 2.Lanzhou Univ Finance & Econ, Sch Informat Engn, Lanzhou 730101, Peoples R China
推荐引用方式 GB/T 7714	Liang, Maolin,Dai, Lifang,Zhao, Ruijuan. Iterative methods for solving tensor equations based on exponential acceleration[J]. NUMERICAL ALGORITHMS,2023.
APA	Liang, Maolin,Dai, Lifang,&Zhao, Ruijuan.(2023).Iterative methods for solving tensor equations based on exponential acceleration.NUMERICAL ALGORITHMS.
MLA	Liang, Maolin,et al."Iterative methods for solving tensor equations based on exponential acceleration".NUMERICAL ALGORITHMS (2023).