A gradient based iterative method and associated preconditioning technique for solving the large multilinear systems, By Saeed Karimi

Research

Title	A gradient based iterative method and associated preconditioning technique for solving the large multilinear systems
Type	Article
Keywords	Multilinear systems, Einstein product, Gradient based, Iterative methods, Preconditioning technique
Journal	CALCOLO
DOI	DOI: 10.1007/s10092-021-00438-1
Researchers	Saeed Karimi (Second researcher)

Abstract

In this paper, a gradient based iterative method and its modified version are proposed for solving a multilinear system or tensor equations. A new preconditioner is presented to accelerate the convergence rate of the new iterative methods. Using the linear operator form of the multilinear system, the new methods can be implemented easily for solving several kinds of tensor equations. Finally, some numerical examples are given to illustrate the effectiveness of the proposed method.