Universally optimal approximation of functionals

Milan Práger

Aplikace matematiky (1979)

  • Volume: 24, Issue: 6, page 406-420
  • ISSN: 0862-7940

Abstract

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A universal optimal in order approximation of a general functional in the space of continuous periodic functions is constructed and its fundamental properties and some generalizations are investigated. As an application the approximation of singular integrals is considered and illustrated by numerical results.

How to cite

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Práger, Milan. "Universally optimal approximation of functionals." Aplikace matematiky 24.6 (1979): 406-420. <http://eudml.org/doc/15119>.

@article{Práger1979,
abstract = {A universal optimal in order approximation of a general functional in the space of continuous periodic functions is constructed and its fundamental properties and some generalizations are investigated. As an application the approximation of singular integrals is considered and illustrated by numerical results.},
author = {Práger, Milan},
journal = {Aplikace matematiky},
keywords = {trigonometric interpolation polynomials; Riesz-Fischer theorem; error functional; trigonometric interpolation polynomials; Riesz-Fischer theorem; error functional},
language = {eng},
number = {6},
pages = {406-420},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Universally optimal approximation of functionals},
url = {http://eudml.org/doc/15119},
volume = {24},
year = {1979},
}

TY - JOUR
AU - Práger, Milan
TI - Universally optimal approximation of functionals
JO - Aplikace matematiky
PY - 1979
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 24
IS - 6
SP - 406
EP - 420
AB - A universal optimal in order approximation of a general functional in the space of continuous periodic functions is constructed and its fundamental properties and some generalizations are investigated. As an application the approximation of singular integrals is considered and illustrated by numerical results.
LA - eng
KW - trigonometric interpolation polynomials; Riesz-Fischer theorem; error functional; trigonometric interpolation polynomials; Riesz-Fischer theorem; error functional
UR - http://eudml.org/doc/15119
ER -

References

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  1. I. Babuška, Über universal optimale Quadraturformeln, Teil 1., Apl. mat. 13 (1968), 304- 338, Teil 2., Apl. mat. 13 (1968), 388-404. (1968) MR0244680
  2. K. Segeth, On universally optimal quadrature formulae involving values of derivatives of integrand, Czech. Math. J. 19 (94) 1969, 605-675. (1969) Zbl0188.13203MR0260177
  3. S. L. Sobolev, Introduction into the theory of cubature formulae, Nauka, Moscow 1974 (pp. 808). (Russian.) (1974) MR0478560
  4. I. P. Natanson, The constructive theory of functions, GITTL, Moscow, Leningrad 1949. (Russian.) (1949) MR0034464

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