Abstract
In this paper we prove a theorem which characterizes a best chebyshev approximation by a weak Markoff system. We give several applications of this result which include best approximation by spline functions.
Zusammenfassung
Ein Theorem, welches eine beste Chebyshev-Approximation durch ein schwaches Markoff-System charakterisiert, wird bewiesen. Mehrere Anwendungen, einschließlich Approximationen durch Spline-Funktionen werden präsentiert.
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References
Cheney, E. W.: Introduction to Approximation Theory. New York: McGraw-Hill. 1966.
Karlin, S.: Total Positivity, Vol. 1. Stanford, Calif.: Stanford University Press. 1968.
Rice, J. R.: Characterization of Chebyshev Approximation by Splines. SIAM J. Numerical Analysis4, 557–567 (1967).
Schumaker, L.: Uniform Approximation by Tchebycheffian Spline Functions. J. of Mathematics and Mechanics18, 369–377 (1969).
Karlin, S.: Total Positivity, Interpolation by Splines, and Green's Functions of Differential Operators. JAT4, 91–112 (1971).
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Micchelli, C.A. Characterization of Chebyshev approximation by weak Markoff systems. Computing 12, 1–8 (1974). https://doi.org/10.1007/BF02239495
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DOI: https://doi.org/10.1007/BF02239495