×

Interpolation by periodic splines with Birkhoff knots. (English) Zbl 0795.41002

Summary: We give a complete characterization of the Hermite interpolation problem by periodic splines with Birkhoff’s knots. As a dual result we derive the characterization of the Birkhoff interpolation by periodic splines with multiple knots. The method of proof is based on a simple reduction of the problem to the non-periodic case.

MSC:

41A05 Interpolation in approximation theory
41A15 Spline approximation
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Bojanov, B.D. (1988): B-splines with Birkhoff knots Constructive Approximation4, 147-156 · Zbl 0683.41019 · doi:10.1007/BF02075455
[2] Hakopian, H., Bojanov, B. (1990): Theory of Spline Functions (in Bulgarian). Nauka i Izkustvo, Sofia
[3] Jetter, K. (1976): Duale Hermite-Birkhoff Probleme J. Approximation Theory17, 119-134 · Zbl 0333.41002 · doi:10.1016/0021-9045(76)90033-2
[4] Korneichuk, N.P. (1984): Splines in approximation theory (in Russian). Nauka, Moscow
[5] Lorentz, G.G., Jetter, K., Riemenschneider, S.D. (1983): Birkhoff interpolation. Encyclopedia of Mathematics and its applications. Vol. 19, Addison-Wisley, Reading, MA · Zbl 0522.41001
[6] Melkman, A. (1974): Interpolation by splines satisfying mixed boundary conditions. Isr. J. Math.19, 369-381 · Zbl 0303.41007 · doi:10.1007/BF02757500
[7] Schumaker, L.L., (1976): Zeros of spline functions and applications. J. Approximation Theory18, 152-168 · Zbl 0339.41003 · doi:10.1016/0021-9045(76)90103-9
[8] Schumaker, L.L. (1981): Spline functions: basic theory. John Wiley and Sons, New York · Zbl 0449.41004
[9] ?ensykbaev, A.A. (1973): Approximation of differentiable periodic functions by splines with uniform partitioning. Mat. Zametki13, (6) 807-816; English translation: Math. Notes (1973)13, 483-489
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.