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The Property of a Special Type of Exponential Spline Function

DOI: 10.4236/apm.2015.513074, PP. 804-807

Keywords: Exponential Spline Function, Interpolation, Error Estimation

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Abstract:

Approximation theory experienced a long term history. Since 50’ last century, the rise of spline function as well as the advance of calculation promotes the growth of classical approximation theory and makes them develop a profound theory in maths, and application values have shown among the field of scientific calculation and engineering technology and etc. At present, the study of spline function had made a great progress and had a lot of fruits, as for that, the reader could look up the book [1] or [2]. Nevertheless, the research staff pays less attention to exponential spline function, since polynomial spline function is a special case of that, so it is much essential and meaningful for one to explore the nature of exponential spline function.

References

[1]  Li, Y.S. (1983) Spline Function and Interpolation. Shanghai Science and Technology Press, Shanghai.
[2]  Feng, Y.Y., Zeng, F.L. and Deng, J.S. (2013) Spine Function and Approximation Theory. University of Science and Technology of China, Hefei.
[3]  Unser, M. and Blu, T. (2005) Cardinal Exponential Splines: Part I—Theory and Filtering Algorithms. IEEE Transactions on Signal Processing, 53, 1425-1438.
http://dx.doi.org/10.1109/TSP.2005.843700
[4]  Zhang, G.Q. and Lin, Y.Q. (1987) Lectures on Functional Analysis. Peking University Press, Beijing.
[5]  Li, Q.Y., Wang, N.C. and Yi, D.Y. (2008) Numerical Analysis. 5th Edition, Tsinghua University Press, Beijing.

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