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Piecewise rational interpolation by witch of Agnesi

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Abstract

The piecewise interpolation method for constructing a smooth curve passing through the sequence of points in the plane is presented. For each section, an interpolation between two points is done by a rational function describing the curve of Agnesi. Conditions of existence of the curve on a section and the methodology for determining its parameters are established. The interpolation error is estimated. The proposed scheme for \(C^1\) rational interpolation can be used to solve the problems of shape preserving interpolation. The described algorithm can be adapted for interpolation of convex, monotonous, or positive datasets. Examples of numeric data are given.

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Authors and Affiliations

  1. Plovdiv University “Paisii Hilendarski”, 139 “Tzar Asen” Str., Plovdiv, Bulgaria

    Tania Yankova

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  1. Tania Yankova
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Correspondence to Tania Yankova.

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Communicated by Antonio José Silva Neto.

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Yankova, T. Piecewise rational interpolation by witch of Agnesi. Comp. Appl. Math. 36, 1205–1216 (2017). https://doi.org/10.1007/s40314-015-0276-6

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  • DOI: https://doi.org/10.1007/s40314-015-0276-6

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