Padé approximants and noise: rational functions

✍ Scribed by Jacek Gilewicz; Maciej Pindor

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 205 KB
• Volume: 105
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(99)00041-2

✦ Synopsis

We continue a study of Padà e approximants (PA) for a series perturbed by random noise -this time we consider more general rational functions. We begin with the simple case of a sum of two geometric series, and then show how these considerations can be extended to a general rational function. We do not study the most general case, but rather concentrate on demonstrating how our results for geometric series extend to new situations encountered when a general rational function is considered. We show that Froissart doublets are a universal feature and we construct an analog of the Froissart polynomial introduced in the earlier paper.