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Fast algorithms for interpolation and smoothing for a general class of fourth order exponential splines

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Abstract

In this work, a general class of interpolation and smoothing natural exponential splines with respect to fourth order differential operators with two real parameters is considered. Some sufficient conditions for the associated matrix \(\textbf{R}\) to be a diagonally dominant matrix are given. Based on these, fast algorithms for computing the coefficients of this general class of exponential splines are developed. The obtained splines have \(C^2\) continuity and are the minimum solution of the combination of interpolation and smoothing energy integral. The performances of the resulting splines in financial data from the S &P500 index are given. Numerical experiments show that the resulting splines have more freedom to adjust the shape and control the energy of the curves. Cross-validation and generalized cross-validation for determining an appropriate smoothing parameter are also given.

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Acknowledgements

The authors gratefully thank the referees and the editor, whose suggestions and comments helped to improve the paper greatly.

Funding

The research is supported by the National Natural Science Foundation of China (Nos. 61802129, 11771453) and the Fundamental Research Funds for the Central Universities (No. 2022ZYGXZR064).

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Authors and Affiliations

  1. School of Mathematics, South China University of Technology, Guangzhou, 510641, Guangdong, People’s Republic of China

    Jiarui Du & Yuanpeng Zhu

  2. Department of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, Guangdong, People’s Republic of China

    Xuli Han

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  1. Jiarui Du
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  2. Yuanpeng Zhu
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Correspondence to Yuanpeng Zhu.

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Du, J., Zhu, Y. & Han, X. Fast algorithms for interpolation and smoothing for a general class of fourth order exponential splines. Numer Algor 94, 1849–1881 (2023). https://doi.org/10.1007/s11075-023-01557-2

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  • DOI: https://doi.org/10.1007/s11075-023-01557-2

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