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.
Highlights
Scalar extrapolation methods have been developed to accelerate the convergence of some sequences of numbers in R or C
In [6], Brezinski proposed a generalization of the scalar e-algorithm for vector sequences called the topological e-algorithm (TEA)
When applied to the sequence generated by the linear relation (32), the TG-reduced rank extrapolation (RRE), TG-minimal polynomial extrapolation (MMPE) and the TG-minimal polynomial extrapolation (MPE) above produce approximations Xk = Tk such that the corresponding residual Rk = B − A ∗ N Tk satisfies the relations
Summary
Scalar extrapolation methods have been developed to accelerate the convergence of some sequences of numbers in R or C. ∆2 s n where the first and the second forward differences are defined by ∆sn = sn+1 − sn and ∆2 sn = ∆sn+1 − ∆sn and in that case we have g1 (n) = ∆sn Such a process was first proposed in 1926 by Aitken in [2]. We consider tensor sequence transformations and propose new tensor extrapolation methods that generalize the classical vector ones.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
