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.
Simulation 2017; 93(3): 185-200 Abir Ben Khaled-El Feki, Laurent Duval, Cyril Faure, Daniel Simon and Mongi Ben Gaid CHOPtrey: Contextual online polynomial extrapolation for enhanced multi-core co-simulation of complex systems Doi: 10.1177/0037549716684026
The influence of calibration data sorting procedures and the order of polynomial curve fit used to calibrate seven hole pressure probes in subsonic, incompressible flow are discussed. It is shown that the inclusion of fourth order polynomial terms is necessary to properly model the physical response of the probe. It is also shown that the uniformity of probe response error is significantly affected by polynomial extrapolation near sector boundaries, and that the uniformity can be improved by using some calibration points in multiple sectors.
The influence of calibration data sorting procedures and the order of polynomial curve fit used to calibrate seven hole pressure probes in subsonic, incompressible flow are discussed. It is shown that the inclusion of fourth order polynomial terms is necessary to properly model the physical response of the probe. It is also shown that the uniformity of probe response error is be significantly affected by polynomial extrapolation near sector boundaries, and that the uniformity can be improved by using some calibration points in multiple sectors.
Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products