Impossibility of fast stable approximation of analytic functions from equispaced samples

Author: 

Platte, RB
Trefethen, LN
Kuijlaars, ABJ

Journal: 

SIAM Review

Publication Date: 

19 September 2011

Last Updated: 

2018-12-08T15:14:06.603+00:00

Issue: 

2

DOI: 

10.1137/090774707

Volume: 

53

page: 

308-318

abstract: 

It is shown that no stable procedure for approximating functions from equally spaced samples can converge exponentially for analytic functions. To avoid instability, one must settle for root-exponential convergence. The proof combines a Bernstein inequality of 1912 with an estimate due to Coppersmith and Rivlin in 1992. © 2011 Society for Industrial and Applied Mathematics.

Symplectic id: 

188461

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article