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Unicity of best mean approximation by second order splines with variable knots. (English) Zbl 0393.41013


MSC:

41A52 Uniqueness of best approximation
41A15 Spline approximation
41A50 Best approximation, Chebyshev systems
Full Text: DOI

References:

[1] D. L. Barrow, C. K. Chui, P. W. Smith, and J. D. Ward, Unicity of best \?\(_{2}\) approximation by second-order splines with variable knots, Bull. Amer. Math. Soc. 83 (1977), no. 5, 1049 – 1050. · Zbl 0372.41007
[2] Carl de Boor, Splines as linear combinations of \?-splines. A survey, Approximation theory, II (Proc. Internat. Sympos., Univ.#Texas, Austin, Tex., 1976) Academic Press, New York, 1976, pp. 1 – 47. · Zbl 0343.41011
[3] C. DE BOOR, ”On the approximation by \( \gamma \) polynomials,” in Approximation with Special Emphasis on Spline Functions , Academic Press, New York, 1969, pp. 157-183.
[4] Dietrich Braess, On the nonuniqueness of monosplines with least \?\(_{2}\)-norm, J. Approximation Theory 12 (1974), 91 – 93. · Zbl 0288.41003
[5] Charles K. Chui, Philip W. Smith, and Joseph D. Ward, On the smoothness of best \?\(_{2}\) approximants from nonlinear spline manifolds, Math. Comp. 31 (1977), no. 137, 17 – 23. · Zbl 0355.41028
[6] Samuel Karlin, Charles A. Micchelli, Allan Pinkus, and I. J. Schoenberg , Studies in spline functions and approximation theory, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. · Zbl 0323.00007
[7] Günter Meinardus, Approximation of functions: Theory and numerical methods, Expanded translation of the German edition. Translated by Larry L. Schumaker. Springer Tracts in Natural Philosophy, Vol. 13, Springer-Verlag New York, Inc., New York, 1967. · Zbl 0152.15202
[8] J. T. Schwartz, Nonlinear functional analysis, Gordon and Breach Science Publishers, New York-London-Paris, 1969. Notes by H. Fattorini, R. Nirenberg and H. Porta, with an additional chapter by Hermann Karcher; Notes on Mathematics and its Applications. · Zbl 0203.14501
[9] Philip W. Smith, On the smoothness of local best \?_{\?} spline approximations, Approximation theory, II (Proc. Internat. Sympos., Univ. Texas, Austin, Tex., 1976) Academic Press, New York, 1976, pp. 563 – 566.
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