Positive Definite Multi-Kernels for Scattered Data Interpolations

Time: 2020-10-10 14:28:56

In this article, we use the knowledge of positive definite tensors to develop a concept of positive definite multi-kernels to construct the kernel-based interpolants of scattered data. By the theorems of reproducing kernel Banach spaces, the optimal recoveries and error analysis of the kernel-based interpolants are shown for a special class of strictly positive definite multi-kernels. 

References:

Qi Ye, Kernel-based probability measures for interpolations, Applied and Computational Harmonic Analysis, 2023, 62 (1), 251-260. DOI: 10.1016/j.acha.2022.09.002

Original version: Interpolations in reproducing kernel Banach spaces by positive definite tensors.