On the stability of rational approximations to the cosine with only imaginary poles

Autor:	Steven M. Serbin, O. A. Karakashian, Laurence A. Bales
Rok vydání:	1988
Předmět:	Computational Mathematics Pure mathematics Degree (graph theory) Numerical approximation Computer Networks and Communications Applied Mathematics Numerical analysis Trigonometric functions Geometry Stability (probability) Software Mathematics Numerical stability
Zdroj:	BIT. 28:651-658
ISSN:	1572-9125 0006-3835
DOI:	10.1007/bf01941140
Popis:	Letr(z) be a rational approximation to cosz with only imaginary poles ±iγ1−1/2, ±iγ2−1/2, ..., ±iγm−1/2 such that |cozz −r(z)| ≤C|z|2m+2 as |z| → 0. If the degree of the numerator ofr(z) is less than or equal to 2m andγi ≥m/4,i=1, ...,m, then we show that |r(z)|≦1 for all realz.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::2f30cbe581efe4c33a49a1af0fd43611 https://doi.org/10.1007/bf01941140 Zobrazit plný text záznamu Full text from SpringerLink