Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T12:36:23.660Z Has data issue: false hasContentIssue false
  • English
  • Français

How close is the approximation by Bernstein polynomials?

Published online by Cambridge University Press:  08 October 2020

G. J. O. Jameson
G. J. O. Jameson*
Affiliation:
Dept. of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF e-mail: g.jameson@lancaster.ac.uk
Get access Rights & Permissions [Opens in a new window]

Extract

A famous theorem of Weierstrass, dating from 1885, states that any continuous function can be uniformly approximated by polynomials on a bounded, closed real interval.

Type
Articles
Information
The Mathematical Gazette , Volume 104 , Issue 561 , November 2020 , pp. 482 - 494
Check for updates
Copyright
© Mathematical Association 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bernstein, S. N., Démonstration du théorème de Weierstrass fondée sur le calcul de probabilités, Comm. Kharkov Math. Soc. 13 (1912).Google Scholar
Rivlin, Theodore J., An introduction to the approximation of functions, Dover (1969).Google Scholar
Bartle, Robert G., The elements of real analysis (2nd edn)., Wiley (1976).Google Scholar
Jameson, G. J. O., Monotonicity of weighted averages of convex functions, Math. Ineq. Appl. 23 (2020) pp. 425–432.Google Scholar
Cheney, E. W., Introduction to approximation theory, McGraw Hill (1966).Google Scholar