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Cardinal Hermite spline interpolation with shifted nodes

Gerlind Plonka, Manfred Tasche

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Abstract

Generalized cardinal Hermite spline interpolation is considered. A special case of this problem is the classical cardinal Hermite spline interpolation with shifted nodes. By means of a corresponding symbol new representations of the cardinal Hermite fundamental splines can be given. Furthermore, a new efficient algorithm for the computation of the cardinal Hermite spline interpolant is obtained, which is mainly based on fast Fourier transform. This algorithm is shown to be also applicable to computing the periodic Hermite spline interpolant. In both cases we only use necessary and sufficient conditions for the existence and uniqueness of the corresponding Hermite spline interpolant.

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What this paper is about

Generalized cardinal Hermite spline interpolation is considered. A special case of this problem is the classical cardinal Hermite spline interpolation with shifted nodes. By means of a corresponding symbol new representations of the cardinal Hermite fundamental splines can be given. Furthermore, a new efficient algorithm for the computation of the cardinal Hermite spline interpolant is obtained, which is mainly based on fast Fourier transform. This algorithm is shown to be also applicable to computing the periodic Hermite spline interpolant. In both cases we only use necessary and sufficient conditions for the existence and uniqueness of the corresponding Hermite spline interpolant.

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Available abstract

Generalized cardinal Hermite spline interpolation is considered. A special case of this problem is the classical cardinal Hermite spline interpolation with shifted nodes. By means of a corresponding symbol new representations of the cardinal Hermite fundamental splines can be given. Furthermore, a new efficient algorithm for the computation of the cardinal Hermite spline interpolant is obtained, which is mainly based on fast Fourier transform. This algorithm is shown to be also applicable to computing the periodic Hermite spline interpolant. In both cases we only use necessary and sufficient conditions for the existence and uniqueness of the corresponding Hermite spline interpolant.

Key concepts: Hermite spline, Cubic Hermite spline, Hermite interpolation, Mathematics, Hermite polynomials, Monotone cubic interpolation, Thin plate spline, Smoothing spline

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