Towards stability results for global radial basis function based quadrature formulas

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