| Title:
|
Optimal discrete approximation of continuous linear operators applicable to control problems (English) |
| Author:
|
Tuzar, Antonín |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
21 |
| Issue:
|
4 |
| Year:
|
1985 |
| Pages:
|
287-297 |
| . |
| Category:
|
math |
| . |
| MSC:
|
41A15 |
| MSC:
|
65D07 |
| MSC:
|
65D25 |
| MSC:
|
65K10 |
| MSC:
|
65L10 |
| MSC:
|
93B40 |
| MSC:
|
93C15 |
| idZBL:
|
Zbl 0591.65017 |
| idMR:
|
MR815616 |
| . |
| Date available:
|
2009-09-24T17:48:28Z |
| Last updated:
|
2012-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125455 |
| . |
| Reference:
|
[1] H. C. Baxвaнов: Численные методы.Hayкa, Mocквa 1973. Zbl 0268.70012 |
| Reference:
|
[2] Z. Beran: Optimalizace diskrétního popisu spojitých systémů v teorii regulace.Candidate of Sciences Thesis, ÚTIA ČSAV, Praha 1980. |
| Reference:
|
[3] M. Golomb: Optimal approximating manifolds in $L_2$2-spaces.J. Math. Anal. Appl. 12 (1965), 505-512. MR 0206588 |
| Reference:
|
[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 0121970 |
| Reference:
|
[5] A. S. B. Holland, B. N. Sahnery: The General Problem of Approximation and Spline Functions.Krieger Publishing Co., Huntington, N. Y. 1979. MR 0547353 |
| Reference:
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[6] T. A. Kilgore: A characterization of the Lagrange interpolating projection with minimal Tchebycheff norm.J. Approx. Theory 24 (1978), 273-288. Zbl 0428.41023, MR 0523977 |
| Reference:
|
[7] P. J. Laurent: Approximation et optimisation.Hermann, Paris 1972. Zbl 0238.90058, MR 0467080 |
| Reference:
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[8] T. Lyche, L. L. Schumaker: Local spline approximation methods.J. Approx. Theory 15 (1975), 294-325. Zbl 0315.41011, MR 0397249 |
| Reference:
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[9] G. Meinardus: Approximation der Funktionen,Theorie und numerische Methoden.Springer-Verlag, Berlin-Gottingen -Heidelberg-New York 1964. MR 0176272 |
| Reference:
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[10] M. J. D. Powell: Approximation Theory and Methods.Cambridge University Press, Cambridge 1981. Zbl 0453.41001, MR 0604014 |
| Reference:
|
[11] A. Sard: Best approximate integration formulae; best approximation formulae.Amer. J. Math. 71 (1949), 80-91. MR 0029283 |
| Reference:
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[12] A. Sard: Optimal approximation.J. Funct. Anal. 1, 2 (1967), 222-244. Zbl 0158.13601, MR 0219967 |
| Reference:
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[13] I. J. Schoenberg: Spline interpolation and best quadrature formulae.Bull. Amer. Math. Soc. 70 (1964), 143-148. Zbl 0136.36202, MR 0157157 |
| Reference:
|
[14] C. Л. Coбoлeв И. Бaбyшкa: Оптимизация численных методов.Aplikace matematiky 10 (1965), 2, 96-129. MR 0191072 |
| Reference:
|
[15] C. Л. Coбoлeв: Введение в теорию кубатурных формул.Hayкa, Mocквa 1974. |
| Reference:
|
[16] J. Stoer, R. Bulirsch: Introduction to Numerical Analysis.Springer-Verlag, Berlin-Heidelberg-New York 1980. Zbl 0553.65004, MR 0557543 |
| Reference:
|
[17] A. Tuzar: Optimal Approximation of Linear Functionals in Hilbert Space with Applications to Numerical Methods.Research Report No. 988, ÚTIA ČSAV, 1979. |
| Reference:
|
[18] A. Tuzar, Z. Beran: Optimization of the discrete description for continuous systems.Problems Control Inform. Theory 10 (1981), 2, 83 - 94. Zbl 0461.41010, MR 0618444 |
| Reference:
|
[19] J. F. Traub, H. Wozniakowski: A General Theory of Optimal Algorithms.Academic Press, New York 1980. Zbl 0441.68046, MR 0584446 |
| Reference:
|
[20] R. Varga: Functional Analysis and Approximation Theory in Numerical Analysis.Society for Industrial and Applied Mathematics, Philadelphia, Pensylvania 1971. Zbl 0226.65064, MR 0310504 |
| . |
