  In this paper, we present a new framework for the recent multidimensional
extrapolation methods: Tensor Global Minimal Polynomial (TG-MPE) and Tensor
Global Reduced Rank Extrapolation (TG-RRE) methods. We develop a new approach
to the one presented in \cite{17}. The proposed framework highlights, in
addition their polynomial feature, the connection of TG-MPE and TG-RRE with
nonlinear Krylov subspace methods. A unified algorithm is proposed for their
implemention. Theoretical results are given and some numerical experiments on
linear and nonlinear problems are considered to confirm the performance of the
proposed algorithms.
