Conjugate gradient-like methods for solving general tensor equation with Einstein product

Tensors have a wide application in data mining, chemistry, information sciences, documents analysis and medical engineering. In this work, we study the general tensor equation Sigma(l)(i=1) F-i *(P) chi *(Q) G(i) = H with Einstein product where F-i, G(i), H, for i = 1, 2, ..., l, are known tensors and chi is an unknown tensor to be determined. The main motivation for this study is the investigation of conjugate gradient-like methods for solving this tensor equation. We show that the conjugate gradient-like methods converge to tensor solutions in a finite number of steps in the absence of round-off errors. Numerical examples confirm 'oretical results and demonstrate the accuracy and computational efficiency of the methods. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.