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Théoremes de caractérisation d’une meilleure approximation dans un espace norme et généralisation de l’algorithme de Remes. (French) Zbl 0161.36202


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[1] Banach, S.: Théorie des operations linéaires. Warsawa: Monografje Matematycne 1932.
[2] Bourbaki, N.: Eléments de Mathématiques. Livre V, Espaces vectoriels topologiques, ch I et II, fasc. 1189, 2eme édition. Paris: Hermann 1966.
[3] —- Eléments de Mathématiques. Livre V, Espaces vectoriels topologiques, ch III, IV, V, fasc. 1229. Paris: Hermann 1964.
[4] Buck, R. C.: Applications of duality in approximation theory. Dans: Approximation of functions (ed.H. L. Garabedian), p. 27–42. Amsterdam-London-New York: Elsevier Publ. Co. 1965. · Zbl 0147.11204
[5] Choquet, G.: Sur la meilleure approximation Bans les espaces normés. Rev. M. Pures et Appliquées (Bucarest)8, 541–542 (1963). · Zbl 0189.12602
[6] Collatz, L.: Approximation von Funktionen bei einer und bei mehreren unabhängigen Veränderlichen. Z. Angew. Math. u. Mech.36, 198–211 (1956). · Zbl 0074.04703 · doi:10.1002/zamm.19560360506
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[10] Meinardus, G.: Approximation von Funktionen und ihre numerische Behandlung. Berlin-Göttingen-Heidelberg: Springer 1964. · Zbl 0124.33103
[11] Rivlin, T. J., andH. S. Shapiro: A unified approach to certain problems of approximation and minimization. J. Soc. Ind. Appl. Math. (SIAM)9, 670–699 (1961). · Zbl 0111.06103 · doi:10.1137/0109056
[12] Singer, I.: Propriet ale suprafetei sferei unitate si applic la rezolvarea problemei unicitatii polinomului de cea mai buna approximatie in spatii Banach oarecare. Studii si cercetari matematice,7, No. 1–2, 1–45 (1956).
[13] —- Caractérisation des éléments de meilleure approximation dans un espace de Banach quelconque. Acte. Sci. Math. Szeged17, 181–189 (1956). · Zbl 0072.13003
[14] Stiefel, E.: Über diskrete und lineare Tschebyscheff-Approximationen. Num. Math.1, 1–28 (1959) · Zbl 0083.11501 · doi:10.1007/BF01386369
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