Mathematical and numerical connections between polynomial extrapolation and Fade approximants: applications in structural mechanics

摘要

This paper deals with the convergence acceleration of a sequence of vectors. This acceleration is achieved by using Minimal Polynomial Extrapolation Method (J Comput Appl Math 2000; 122: 149-165) or by the vectorial Pade approximants, that have been considered in the framework of high-order iterative algorithms (Commun Numer Methods Eng 1999; 15:701-708; Comput Methods Appl Mech Eng 2000; 190:1845-1858). It is established that, in some cases, these two procedures are mathematically equivalent. In the practice, such techniques are affected by numerical instabilities. So the numerical robustness of the two methods is discussed, on the basis of a test emanating from non-linear elastic thin shell analysis.