Multiquadric trigonometric spline quasi-interpolation for numerical differentiation of noisy data: a stochastic perspective
type: Item
instance of: scholarly article
title: Multiquadric trigonometric spline quasi-interpolation for numerical differentiation of noisy data: a stochastic perspective
zbMATH Open document ID: 1421.65007
author: Juan-Miguel Gracia
published in: Numerical Algorithms
publication date: 2018-01-19T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 65T40
zbMATH DE Number: 6827924
zbMATH Keywords: numerical differentiation of noisy data
zbMATH Keywords: multiquadric trigonometric spline quasi-interpolation
zbMATH Keywords: asymptotic property
zbMATH Keywords: bandwidth selection
zbMATH Keywords: kernel regression
reviewed by: Aurelian Bejancu
MaRDI profile type: Publication
full work available at URL: s11075-017-0313-1
OpenAlex ID: W2598540729
cites work: A general method for constructing quasi-interpolants from B-splines
cites work: Computing quasi-interpolants from the B-form of B-splines
cites work: A‐posteriori error estimates for the finite element method
cites work: Near-best univariate spline discrete quasi-interpolants on nonuniform partitions
cites work: Increasing the approximation order of spline quasi-interpolants
cites work: A general spline differential quadrature method based on quasi-interpolation
cites work: Multiquadric \(B\)-splines
cites work: Univariate multiquadric approximation: Quasi-interpolation to scattered data
cites work: Convergence of Univariate Quasi-Interpolation Using Multiquadrics
cites work: On quasi-interpolation with radial basis functions
cites work: Pointwise approximation with quasi-interpolation by radial basis functions
cites work: Nonparametric estimation of a regression function
cites work: Quasi-interpolation in isogeometric analysis based on generalized B-splines
cites work: Approximating partial derivatives of first and second order by quadratic spline quasi-interpolants on uniform meshes
cites work: Q5432198
cites work: Quadratic spline quasi-interpolants and collocation methods
cites work: Quasi-interpolation for linear functional data
cites work: A quasi-interpolation scheme for periodic data based on multiquadric trigonometric B-splines
cites work: Approximation orders and shape preserving properties of the multiquadric trigonometric B-spline quasi-interpolant
cites work: Q3339943
cites work: Quasi-interpolation in Riemannian manifolds
cites work: Local asymptotics for polynomial spline regression
cites work: A new version of the Strang--Fix conditions
cites work: Q5409194
cites work: Q5524944
cites work: Finding Numerical Derivatives for Unstructured and Noisy Data by Multiscale Kernels
cites work: Quasi-interpolants based on trigonometric splines
cites work: Approximation to the \(k\)-th derivatives by multiquadric quasi-interpolation method
cites work: Stability of multiquadric quasi-interpolation to approximate high order derivatives
cites work: Quadratic spline quasi-interpolants on Powell-Sabin partitions
cites work: Bandwidth choice and confidence intervals for derivatives of noisy data
cites work: An introduction to Schoenberg's approximation
cites work: Q5316365
cites work: Numerical integration based on bivariate quadratic spline quasi-interpolants on Powell-Sabin partitions
cites work: Chordal Cubic Spline Quasi Interpolation
cites work: A Spline Product Quasi-interpolation Method for Weakly Singular Fredholm Integral Equations
cites work: Smoothing noisy data with spline functions
cites work: Reconstruction of numerical derivatives from scattered noisy data
cites work: Shape preserving properties and convergence of univariate multiquadric quasi-interpolation
cites work: Generalized Strang-Fix condition for scattered data quasi-interpolation
cites work: Sampling scattered data with Bernstein polynomials: stochastic and deterministic error estimates
cites work: Conservative multiquadric quasi-interpolation method for Hamiltonian wave equations
DOI: 10.1007/S11075-017-0313-1
description: scientific article; zbMATH DE number 6827924