Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products

Abstract

In this paper, we present new Tensor extrapolation methods as generalizations of well known vector, matrix and block extrapolation methods such as polynomial extrapolation methods or ϵ-type algorithms. We will define new tensor products that will be used to introduce global tensor extrapolation methods. We discuss the application of these methods to the solution of linear and non linear tensor systems of equations and propose an efficient implementation of these methods via the global-QR decomposition.

Keywords

• Einstein product
• Krylov subspaces
• sequence transformation
• tensor extrapolation