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2001•International Journal of Computer MathematicsRequires access

A discrete trigonometric interpolation method

Tianzi Jiang, David Evans

Open publisher page 2 citations

Abstract

Interpolation theory is a necessary and crucial tool for many applied engineering sciences.In this paper, we propose a new kind of 2-period interpolation of functions with period 2π at the nodes x k = x k,n = kπ/n, (k = 0,1,…, 2n − 1).We find out the necessary and sufficient conditions for regularity of this new interpolation problem.Moreover, a closed form expression for the interpolation polynomial is given.Our interpolation is of more practical significance.Our results provide the theoretical basis for using our interpolation in practical problems.

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What this paper is about

Interpolation theory is a necessary and crucial tool for many applied engineering sciences.In this paper, we propose a new kind of 2-period interpolation of functions with period 2π at the nodes x k = x k,n = kπ/n, (k = 0,1,…, 2n − 1).We find out the necessary and sufficient conditions for regularity of this new interpolation problem.Moreover, a closed form expression for the interpolation polynomial is given.Our interpolation is of more practical significance.Our results provide the theoretical basis for using our interpolation in practical problems.

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Available abstract

Interpolation theory is a necessary and crucial tool for many applied engineering sciences.In this paper, we propose a new kind of 2-period interpolation of functions with period 2π at the nodes x k = x k,n = kπ/n, (k = 0,1,…, 2n − 1).We find out the necessary and sufficient conditions for regularity of this new interpolation problem.Moreover, a closed form expression for the interpolation polynomial is given.Our interpolation is of more practical significance.Our results provide the theoretical basis for using our interpolation in practical problems.

Key concepts: Trigonometric interpolation, Interpolation (computer graphics), Polynomial interpolation, Bilinear interpolation, Mathematics, Birkhoff interpolation, Spline interpolation, Stairstep interpolation

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