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

作　　者：Raziyeh Erfanifar Masoud Hajarian Khosro Sayevand 

机构地区：[1]Department of Applied Mathematics,Faculty of Mathematical Sciences,Shahid Beheshti University,Tehran,Iran [2]Faculty of Mathematics and Statistics,Malayer University,Malayer,Iran

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2024年第1期69-92,共24页高等学校计算数学学报（英文版）

基　　金：funded by Iran National Science Foundation(INSF)under project No.4013447.

摘　　要：This study aims to investigate the polar decomposition of tensors with the Einstein product for thefirst 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 forfinding 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 tofind 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 

分 类 号：O183.2[理学—数学]