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

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37-68,共32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：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 compar-isons 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=B.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 

分 类 号：O17[理学—数学]