Journal article

Authors list: Ortmann, Mathis; Buhmann, Martin

Publication year: 2024

Journal: Journal of Mathematical Analysis and Applications

Volume number: 538

Issue number: 1

ISSN: 0022-247X

eISSN: 1096-0813

Open access status: Hybrid

DOI Link: https://doi.org/10.1016/j.jmaa.2024.128359

Publisher: Elsevier

Abstract: 
A new generalization of multiquadric functions phi ( x ) = root c(2d) + || x ||(2d) , where x is an element of R-n , c is an element of R, d is an element of N, is presented to increase the accuracy of quasi -interpolation further. With the restriction to Euclidean spaces of odd dimensionality, the generalization can be used to generate a quasi -Lagrange operator that reproduces all polynomials of degree 2 d - 1. In contrast to the classical multiquadric, the convergence rate of the quasi -interpolation operator can be significantly improved by a factor h(2d -n - 1) , where h > 0 represents the grid spacing. Among other things, we compute the generalized Fourier transform of this new multiquadric function. Finally, an infinite regular grid is employed to analyse the properties of the aforementioned generalization in detail. We also present numerical results to demonstrate the advantages of our new multiquadric functions. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

Harvard Citation style: Ortmann, M. and Buhmann, M. (2024) High accuracy quasi-interpolation using a new class of generalized multiquadrics, Journal of Mathematical Analysis and Applications, 538(1), Article 128359. https://doi.org/10.1016/j.jmaa.2024.128359

APA Citation style: Ortmann, M., & Buhmann, M. (2024). High accuracy quasi-interpolation using a new class of generalized multiquadrics. Journal of Mathematical Analysis and Applications. 538(1), Article 128359. https://doi.org/10.1016/j.jmaa.2024.128359