Summary The performance of adaptive estimators that employ embedding in reproducing kernel Hilbert spaces (RKHS) depends on the choice location basis centers. Parameter convergence and error approximation rates depend where how centers are distributed state‐space. In this article, we develop theory relates parameter to position We criteria for choosing a specific class systems by exploiting fac...

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy NONLINEAR SIGNAL PROCESSING BASED ON REPRODUCING KERNEL HILBERT SPACE By Jianwu Xu December 2007 Chair: Jose C. Principe Major: Electrical and Computer Engineering My research aimed at analyzing the recently proposed correntropy function...

Kernel function, which allows the formulation of nonlinear variants of any algorithm that can be cast in terms of dot products, makes the Support Vector Machines (SVM) have been successfully applied in many fields, e.g. classification and regression. The importance of kernel has motivated many studies on its composition. It’s well-known that reproducing kernel (R.K) is a useful kernel function ...

We establish asymptotic formulas for polynomials that are orthogonal over the unit disk with respect to a weight of the form |w(z)|2, where w(z) is a polynomial without zeros on the unit circle |z| = 1. The formulas put in evidence a strong connection between the behavior of the polynomials and the reproducing kernel of an associated weighted Bergman space, which produces interesting new featur...

The purpose of this article is to present a brief exposition of the role of Riccati equations in the theory of reproducing kernel spaces. In particular, we shall exhibit a connection between positive semidefinite solutions of matrix Riccati equations and a class of finite dimensional reproducing kernel Hilbert spaces of rational vector valued functions, and an analogous (but more general) conne...

Volterra and Wiener series are perhaps the best-understood nonlinear system representations in signal processing. Although both approaches have enjoyed a certain popularity in the past, their application has been limited to rather low-dimensional and weakly nonlinear systems due to the exponential growth of the number of terms that have to be estimated. We show that Volterra and Wiener series c...

Oh et al ([25]) introduced the reproducing polynomial particle (RPP) shape functions that are piecewise polynomial and satisfy the Kronecker delta property. In this paper, we introduce RPPM (Reproducing Polynomial Particle Methods) that is the Galerkin approximation method associated with the use of the RPP approximation space. Planting particles in the computation domain in a patchwise uniform...