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Multiquadric trigonometric spline quasi-interpolation for numerical differentiation of noisy data: a stochastic perspective

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Abstract

Based on multiquadric trigonometric spline quasi-interpolation, the paper proposes a scheme for numerical differentiation of noisy data, which is a well-known ill-posed problem in practical applications. In addition, in the perspective of kernel regression, the paper studies its large sample properties including optimal bandwidth selection, convergence rate, almost sure convergence, and uniformly asymptotic normality. Simulations are provided at the end of the paper to demonstrate features of the scheme. Both theoretical results and simulations show that the scheme is simple, easy to compute, and efficient for numerical differentiation of noisy data.

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Acknowledgments

We wish to express our great gratitude to the referees for their valuable comments and suggestions.

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Correspondence to Ran Zhang.

Additional information

This work is supported by NSFC (11501006, 61672032), NSFC Key Project (91330201), SGST (12DZ 2272800), Joint Research Fund by National Natural Science Foundation of China and Research Grants Council of Hong Kong (11461161006), Fund of Introducing Leaders of Science and Technology of Anhui University (J10117700057) the 4th Project of Cultivating Backbone of Young Teachers of Anhui University (J01005138), and Anhui Provincial Science and Technology Major Project (16030701091).

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Gao, W., Zhang, R. Multiquadric trigonometric spline quasi-interpolation for numerical differentiation of noisy data: a stochastic perspective. Numer Algor 77, 243–259 (2018). https://doi.org/10.1007/s11075-017-0313-1

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  • DOI: https://doi.org/10.1007/s11075-017-0313-1

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