Construction of multivariate polynomial approximation kernels via semidefinite programming

TL;DR

This paper develops a hierarchy of multivariate polynomial approximation kernels using semidefinite programming, providing implementation details and techniques for symmetry reduction to enhance computational efficiency.

Contribution

It introduces a novel hierarchy of kernels constructed via semidefinite programming, with methods to improve numerical tractability through symmetry reduction.

Findings

Successful construction of polynomial approximation kernels

Implementation details for semidefinite programs provided

Symmetry reduction improves numerical tractability

Abstract

In this paper we construct a hierarchy of multivariate polynomial approximation kernels via semidefinite programming. We give details on the implementation of the semidefinite programs defining the kernels. Finally, we show how a symmetry reduction may be performed to increase numerical tractability.