Multiquadric trigonometric spline quasi-interpolation for numerical differentiation of noisy data: a stochastic perspective
The multiquadric trigonometric kernel was defined by \textit{W. Gao} and \textit{Z. Wu} [J. Comput. Appl. Math. 271, 20--30 (2014; Zbl 1326.65021)] as \(\phi(x)=\sqrt{c^2 + \sin^2 (x/2)}\), where \(c\) is a nonnegative shape parameter. The paper under review proposes a quasi-interpolation method for numerical differentiation of noisy data, based on the above multiquadric trigonometric kernel. The main results concern the optimal choice of the shape parameter minimizing the corresponding mean squared error, as well as the almost sure convergence and uniform asymptotic normality of the quasi-interpolant. Two numerical examples are presented, which demonstrate a better performance of the proposed method when compared to trigonometric spline quasi-interpolation and to central divided differences.
multiquadric trigonometric spline quasi-interpolation
scientific article; zbMATH DE number 6827924
scientific article