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Práger, Milan
Universally optimal approximation of functionals. (English). Aplikace matematiky, vol. 24 (1979), issue 6, pp. 406-420
MSC: 30E20, 41A10, 41A15, 41A25, 41A30, 41A55, 65D15, 65D32 | MR 0547044 | Zbl 0449.41003 | DOI: 10.21136/AM.1979.103824
Keywords:
trigonometric interpolation polynomials; Riesz-Fischer theorem; error functional
Summary:
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.
References:
[1] I. Babuška: Über universal optimale Quadraturformeln. Teil 1., Apl. mat. 13 (1968), 304- 338, Teil 2., Apl. mat. 13 (1968), 388-404. MR 0244680
[2] K. Segeth: On universally optimal quadrature formulae involving values of derivatives of integrand. Czech. Math. J. 19 (94) 1969, 605-675. MR 0260177 | Zbl 0188.13203
[3] S. L. Sobolev: Introduction into the theory of cubature formulae. Nauka, Moscow 1974 (pp. 808). (Russian.) MR 0478560
[4] I. P. Natanson: The constructive theory of functions. GITTL, Moscow, Leningrad 1949. (Russian.) MR 0034464
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