Positive Definite Multi-Kernels for Scattered Data Interpolations

TL;DR

This paper introduces positive definite multi-kernels for scattered data interpolation, leveraging tensor properties and reproducing kernel Banach spaces to improve kernel-based interpolation accuracy and analysis.

Contribution

It develops a new class of positive definite multi-kernels and analyzes their optimal recovery and error bounds for scattered data interpolation.

Findings

Established a framework for positive definite multi-kernels

Derived error bounds for kernel-based interpolants

Enhanced understanding of scattered data interpolation techniques

Abstract

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 techniques 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.