Geodesic
Optimal discrete approximation of continuous linear operators applicable to control problems
Kybernetika, Tome 21 (1985) no. 4, pp. 287-297

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Classification : 41A15, 65D07, 65D25, 65K10, 65L10, 93B40, 93C15 
Tuzar, Antonín. Optimal discrete approximation of continuous linear operators applicable to control problems. Kybernetika, Tome 21 (1985) no. 4, pp. 287-297. http://geodesic.mathdoc.fr/item/KYB_1985_21_4_a4/
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     zbl = {0591.65017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1985_21_4_a4/}
}
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[1] H. C. Baxвaнов: Численные методы. Hayкa, Mocквa 1973. | Zbl

[2] Z. Beran: Optimalizace diskrétního popisu spojitých systémů v teorii regulace. Candidate of Sciences Thesis, ÚTIA ČSAV, Praha 1980.

[3] M. Golomb: Optimal approximating manifolds in $L_2$2-spaces. J. Math. Anal. Appl. 12 (1965), 505-512. | MR

[4] M. Golomb, and H. Weinberger: Optimal approximation and erros bounds. In: On Numerical Approximation (R. E. Langer, ed.), Univ. of Wisconsin Press, Madison 1959, pp. 117-190. | MR

[5] A. S. B. Holland, B. N. Sahnery: The General Problem of Approximation and Spline Functions. Krieger Publishing Co., Huntington, N. Y. 1979. | MR

[6] T. A. Kilgore: A characterization of the Lagrange interpolating projection with minimal Tchebycheff norm. J. Approx. Theory 24 (1978), 273-288. | MR | Zbl

[7] P. J. Laurent: Approximation et optimisation. Hermann, Paris 1972. | MR | Zbl

[8] T. Lyche, L. L. Schumaker: Local spline approximation methods. J. Approx. Theory 15 (1975), 294-325. | MR | Zbl

[9] G. Meinardus: Approximation der Funktionen,Theorie und numerische Methoden. Springer-Verlag, Berlin-Gottingen -Heidelberg-New York 1964. | MR

[10] M. J. D. Powell: Approximation Theory and Methods. Cambridge University Press, Cambridge 1981. | MR | Zbl

[11] A. Sard: Best approximate integration formulae; best approximation formulae. Amer. J. Math. 71 (1949), 80-91. | MR

[12] A. Sard: Optimal approximation. J. Funct. Anal. 1, 2 (1967), 222-244. | MR | Zbl

[13] I. J. Schoenberg: Spline interpolation and best quadrature formulae. Bull. Amer. Math. Soc. 70 (1964), 143-148. | MR | Zbl

[14] C. Л. Coбoлeв И. Бaбyшкa: Оптимизация численных методов. Aplikace matematiky 10 (1965), 2, 96-129. | MR

[15] C. Л. Coбoлeв: Введение в теорию кубатурных формул. Hayкa, Mocквa 1974.

[16] J. Stoer, R. Bulirsch: Introduction to Numerical Analysis. Springer-Verlag, Berlin-Heidelberg-New York 1980. | MR | Zbl

[17] A. Tuzar: Optimal Approximation of Linear Functionals in Hilbert Space with Applications to Numerical Methods. Research Report No. 988, ÚTIA ČSAV, 1979.

[18] A. Tuzar, Z. Beran: Optimization of the discrete description for continuous systems. Problems Control Inform. Theory 10 (1981), 2, 83 - 94. | MR | Zbl

[19] J. F. Traub, H. Wozniakowski: A General Theory of Optimal Algorithms. Academic Press, New York 1980. | MR | Zbl

[20] R. Varga: Functional Analysis and Approximation Theory in Numerical Analysis. Society for Industrial and Applied Mathematics, Philadelphia, Pensylvania 1971. | MR | Zbl