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Keywords:
Interpolation; trigonometric polynomial; regularity; computer vision
Interpolation; trigonometric polynomial; regularity; computer vision
Summary:
It is well-known that the interpolation theory plays an important role in many fields of computer vision, especially in surface reconstruction. In this paper, we introduce a new kind of 2-period interpolation of functions with period $2\pi $. 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 practical significance. Our results provide the theoretical basis for using our interpolation in practical problems.
References:
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[s2] A. Sharmea, J. Szabados and R.S. Varga: 2-periodic lacunary trigonometric interpolation: $(0,M)$ case. Proc. Conf. on Constructive Theory of Functions’87, Varna, Bulgaria, pp. 420–426.
[s3] A. Sharmea, Sun Xiehua: A 2-periodic Trigonometric Interpolation Problem. Approx. Theory and its Appl. 8 (1992), no. 4, 1–16. MR 1212842
[s4] J. Szabados: On the Rate of Convergence of a Lacunary Trigonometric interpolation Process. Acta Math. Hungar. 47 (1986), 361–370. DOI 10.1007/BF01953973 | MR 0854522 | Zbl 0694.42006
[s5] Liu Yongping: On the trigonometric interpolation and the entire interpolation. Approx. Theory and its Appl. 6 (1990), no. 4, 85–106. MR 1106069 | Zbl 0724.42005
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