Computation of the -Table Related to the Padé Approximation

Abstract

The aim of this paper is to give a complete and practical method for numerical application of Padé approximation with the help of the -table analysis. We present an exhaustive list of useful formulas to compute a -table related to a formal power series . Some of these formulas are not widely known, because they were presented in publications of limited circulation. Some others were never published, as three symmetric Paszkowski-like formulas to overcome the blocks in a -table or an extension of local error formula for Padé approximants in the blocks. All formulas are given in two versions: in terms of Toeplitz determinants (-table) and in the version of Hankel determinants (-table). We compare the theory with numerical observations by reproducing different computational aspects of software producing the -tables with the presence of blocks and their evolution following the evolution of computer environment.