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Third-order accurate monotone cubic Hermite interpolants. (English) Zbl 1411.65022

Summary: Monotonicity-preserving interpolants are used in several applications as engineering or computer aided design. In last years some new techniques have been developed. In particular, in [the first author, SIAM J. Numer. Anal. 51, No. 5, 2613–2633 (2013; Zbl 1282.41001)] some new methods to design monotone cubic Hermite interpolants for uniform and non-uniform grids are presented and analyzed. They consist on calculating the derivative values introducing the weighted harmonic mean and a non-linear variation. With these changes, the methods obtained are third-order accurate, except in extreme situations. In this paper, a new general mean is used and a third-order interpolant for all cases is gained. We perform several experiments comparing the known techniques as the method proposed by F. N. Fritsch and J. Butland [SIAM J. Sci. Stat. Comput. 5, 300–304 (1984; Zbl 0577.65003)] using the Brodlie’s function, PCHIP program of Matlab [C. B. Moler, Numerical computing with Matlab. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2004; Zbl 1059.68162); G. Wolberg and I. Alfy, J. Comput. Appl. Math. 143, No. 2, 145–188 (2002; Zbl 1001.65012)] with the new algorithm.

MSC:

65D05 Numerical interpolation
41A05 Interpolation in approximation theory

Software:

Matlab; pchip
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Full Text: DOI

References:

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