Towards stability of radial basis function based cubature formulas

08/13/2021
by   Jan Glaubitz, et al.
0

Cubature formulas (CFs) based on radial basis functions (RBFs) have become an important tool for multivariate numerical integration of scattered data. Although numerous works have been published on such RBF-CFs, their stability theory can still be considered as underdeveloped. Here, we strive to pave the way towards a more mature stability theory for RBF-CFs. In particular, we prove stability for RBF-CFs based on compactly supported RBFs under certain conditions on the shape parameter and the data points. Moreover, it is shown that asymptotic stability of many RBF-CFs is independent of polynomial terms, which are often included in RBF approximations. While our findings provide some novel conditions for stability of RBF-CFs, the present work also demonstrates that there are still many gaps to fill in future investigations.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

04/07/2022

Energy-stable global radial basis function methods on summation-by-parts form

Radial basis function methods are powerful tools in numerical analysis a...
01/24/2021

Towards Stable Radial Basis Function Methods for Linear Advection Problems

In this work, we investigate (energy) stability of global radial basis f...
08/11/2020

A Neumann series of Bessel functions representation for solutions of the radial Dirac system

A new representation for a regular solution of the radial Dirac system o...
10/27/2021

Stability estimates for radial basis function methods applied to time-dependent hyperbolic PDEs

We derive stability estimates for three commonly used radial basis funct...
05/12/2021

Construction and comparative study of Euler method with adaptive IQ and IMQ-RBFs

The fundamental purpose of the present work is to constitute an enhanced...
08/19/2019

Divide and Congruence III: From Decomposition of Modal Formulas to Preservation of Stability and Divergence

In two earlier papers we derived congruence formats with regard to trans...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.