Best uniform rational approximation ofxα on [0, 1]

By Herbert Stahl. 2003

106 citations recorded by the source corpus.

A strong error estimate for the uniform rational approximation of xa on [0, 1] is given, and its proof is sketched. Let E„n(xa, [0, 1]) denote the minimal approximation error in the uniform norm. Then it is shown that lim e2*^"Enn(xa , [0, 1]) = 41+a| sin7ta| n—»oo holds true for each a > 0 .

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/b162dd58a2271446b0f13a34a6eece5af1716acf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

On the efficient computation of high-dimensional integrals and the approximation by exponential sums (2009, methodology): “It is based on a result of Vjay ceslavov [29] which in turn requires complicated evaluations of some special integrals; see also [ 25 ].”
The AAA Algorithm for Rational Approximation (2016, background): “The precise convergence rate for minimax (best L ∞ ) approximations was eventually shown to be E nn ( | x | ) ∼ 8 exp( − π √ n ) [55].”
Nikishin Systems Are Perfect (2010, background): “Stahl’s theorem, see [50], on the best rational approximation of x on [0,1].”
The Exponentially Convergent Trapezoidal Rule (2014, unknown): “Later Stahl found the precise asymptotic behavior [154]: Enn(|ξ|) ∼ 8e−π √ .”