Computation of thec-Table Related to the Padé Approximation

[摘要] The aim of this paper is to give a complete and practical method for numerical application of Padé approximation with the help of thec-table analysis. We present an exhaustive list of useful formulas to compute ac-table related to a formal power seriesC(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 ac-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 reproducingdifferent computational aspects ofsoftwareproducing thec-tables with the presence of blocks and their evolutionfollowing the evolution of computer environment.

[学科分类] 应用数学