Recursive computation of Padé-Legendre approximants and some acceleration properties

@article{Matos2001RecursiveCO,
title={Recursive computation of Pad{\'e}-Legendre approximants and some acceleration properties},
author={Ana Cristina C Matos},
journal={Numerische Mathematik},
year={2001},
volume={89},
pages={535-560}
}

In this paper, after recalling the two definitions of the generalizations of the Pad́ e approximants to orthogonal series, we will define the Pad́e–Legendre approximants of a Legendre series. We will propose two algorithms for the recursive computation of some sequences of these approximants. We will also estimate the speed of convergence of the columns of the Pad́e–Legendre table from the asymptotic behaviour of the coefficients of the Legendre series. Finally we will illustrate these results… CONTINUE READING