Yu. S. Volkov, V. V. Bogdanov, V. L. Miroshnichenko, V. T. Shevaldin, “Shape-Preserving Interpolation by Cubic Splines”, Mat. Zametki, 2010, Volume 88, Issue 6,Pages <nobr>836

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Shape-Preserving Interpolation by Cubic Splines

Yu. S. Volkov^ab, V. V. Bogdanov^a, V. L. Miroshnichenko^ab, V. T. Shevaldin^c

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Novosibirsk State University
^c Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: We consider the problem of shape-preserving interpolation by cubic splines. We propose a unified approach to the derivation of sufficient conditions for the $k$‑monotonicity of splines (the preservation of the sign of any derivative) in interpolation of $k$-monotone data for $k=0,\dots,4$.

Keywords: cubic spline, shape-preserving interpolation, $k$‑monotonicity, $B$-spline, matrix with diagonal dominance.

UDC: 517.518.8

Received: 01.11.2008

DOI: 10.4213/mzm6576