两个基于不同张量乘法的四阶张量分解

摘要

提出了两个基于不同张量乘法的四阶张量分解.首先,在矩阵乘法的基础上,定义第一种四阶张量乘法(F-乘),基于F-乘提出了第一种四阶张量分解(F-TD).其次,基于三阶张量t-product给出了第二种四阶张量乘法(B-乘)和分解(FT-SVD).同时,利用两种分解方法,分别给出两个张量逼近定理.最后,三个数值算例阐明提出的两种分解方法的准确性和可行性.%In this paper,two factorizations for fourth-order tensors based on different multiplications of the fourth-order tensors are investigated.One is,called as F-TD,based on the fourth-order tensor multiplication (F-product).Another is,the fourth-order tensor multiplication and decomposition are defined,called as B-product and FT-SVD,based on the t-product of the third-order tensor multiplication.Meanwhile,two tensor approximation theorems are present using two decomposition methods.Finally,three numerical examples are given to demonstrate the accuracy and the feasibility of our proposed methods.