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Rational approximation of $x^n$
- Publication Year :
- 2018
-
Abstract
- Let $E_{kk}^{(n)}$ denote the minimax (i.e., best supremum norm) error in approximation of $x^n$ on $[\kern .3pt 0,1]$ by rational functions of type $(k,k)$ with $k<n$. We show that in an appropriate limit $E_{kk}^{(n)} \sim 2\kern .3pt H^{k+1/2}$ independently of $n$, where $H \approx 1/9.28903$ is Halphen's constant. This is the same formula as for minimax approximation of $e^x$ on $(-\infty,0\kern .3pt]$.<br />Comment: 5 pages
- Subjects :
- Mathematics - Numerical Analysis
41A20
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1801.01092
- Document Type :
- Working Paper