Computation of the c-Table Related to the Padé Approximation

Abstract EN

The aim of this paper is to give a complete and practical method for numerical application of Padé approximation with the help of the c-table analysis.

We present an exhaustive list of useful formulas to compute a c-table related to a formal power series C(z)=∑n=0∞cnzn.

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 c-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 (c-table) and in the version of Hankel determinants (c-table).

We compare the theory with numerical observations by reproducing different computational aspects of software producing the c-tables with the presence of blocks and their evolution following the evolution of computer environment.