The Best Multipoint Padé Approximant. (26th October 2018)

• Record Type: Journal Article
• Authors: Levis, Fabian Eduardo; Rodriguez, Claudia N.
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 14(2018)
• Page Start: 1495
• Page End: 1513
• Publication Date: 2018-10-26
• Subjects: Best approximation -- complex domain -- Padé approximant -- weighted Lp-spaces; 41A30 -- 41A21; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1485696
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: This paper is dealing with the problem of finding the "best" multipoint Padé approximant of an analytic function when data in some neighborhoods of sampling points are more important than others. More exactly, we obtain a multipoint Padé approximants as limits of best rational L p -approximations on union of disks, when the measure of them tends to zero with different speeds. As such, this technique provides useful qualitative and analytic information concerning the approximants, which is difficult to obtain from a strictly numerical treatment.