N-mode Minimal Tensor Extrapolation Methods

Abstract The purpose of this work is to present, using the n-mode product, a new approach to generalize, for tensor sequence,s the well-known vector extrapolation methods MPE ( Minimal Polynomial Extrapolation method) and RRE (Reduced Rank Extrapolation method). We define the notion of the n-mode minimal polynomial of a matrix with respect to a tensor. This polynomial will be used, through the iterative solution of some tensor linear systems, to introduce the tensor version of MPE and RRE. These methods involve only the terms of sequences that result from the used iterative methods. The implementation of these methods on some sequences of tensors confirms the effectiveness and applicability of our approach.