Highly localized kernels constructed by orthogonal polynomials have been fundamental in the recent development of approximation and computational analysis on unit sphere, ball, several other regular domains. In this work, we first study homogeneous spaces that are assumed to contain highly establish a framework for tight frames such spaces, which extends works bounded We then show is applicable...

This paper is concerned with the stabilization problem for nonlinear systems. A new polynomial-approximation-based approach for modeling nonlinear systems is first proposed. The nonlinearity is approximated by polynomials and the approximation errors are treated as modeling uncertainties. The original nonlinear systems are converted into polynomial systems with modeling uncertainties. In order ...

In this paper, we consider approximation algorithms for optimizing a generic multivariate polynomial function in discrete (typically binary) variables. Such models have natural applications in graph theory, neural networks, error-correcting codes, among many others. In particular, we focus on three types of optimization models: (1) maximizing a homogeneous polynomial function in binary variable...