Volume 52, pp. 113-131, 2020.

Fractional Hermite interpolation for non-smooth functions

Jiayin Zhai, Zhiyue Zhang, and Tongke Wang


The interpolation of functions plays a fundamental role in numerical analysis. The highly accurate approximation of non-smooth functions is a challenge in science and engineering as traditional polynomial interpolation cannot characterize the singular features of these functions. This paper aims at designing a fractional Hermite interpolation for non-smooth functions based on the local fractional Taylor expansion and at deriving the corresponding explicit formula and its error remainder. We also present a piecewise hybrid Hermite interpolation scheme, a combination of fractional Hermite interpolation and traditional Hermite interpolation. Some numerical examples are presented to show the high accuracy of the fractional Hermite interpolation method.

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Key words

non-smooth function, local fractional Taylor expansion, fractional Hermite interpolation, error remainder

AMS subject classifications

26A30, 41A05, 65D05, 97N50

Links to the cited ETNA articles

[20]Vol. 45 (2016), pp. 476-498 Mohammad Masjed-Jamei and Gradimir V. Milovanović: Weighted Hermite quadrature rules

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