Hosvd-tmpe: an extrapolation method for multidimensional sequences

Accelerating slowly convergent sequences is one of the main purposes of extrapolation methods. In this paper, we present a new tensor polynomial extrapolation method, which is based on a modified minimisation problem and some ideas leading to the recent Tensor Global Minimal Extrapolation Method (TG-MPE). We discuss the application of our method to fixed-point iterative process. An efficient algorithm via the higher order Singular Value Decomposition (HOSVD) is proposed for its implementation. The numerical tests show clearly the effectiveness and performance of the proposed method.