where x(t) ∈ D ⊂ Rp and f (x) ∈ R is an unknown function but assumed to be bounded function in x. When the structure of the uncertainty is unknown, function approximation is usually employed to estimate the unknown function. In recent years, neural networks have gained a lot of attention in function approximation theory in connection with adaptive control. Multi-layer neural networks have the c...

In this paper we propose a new technique for the identification of NARX Hammerstein systems. The new technique is based on the theory of Least Squares Support Vector Machines function-approximation and allows to determine the memoryless static nonlinearity as well as the linear model parameters. As the technique is non-parametric by nature, no assumptions about the static nonlinearity need to b...

Clustering techniques have always been oriented to solve classification and pattern recognition problems. This clustering techniques have been used also to initialize the centers of the Radial Basis Function (RBF) when designing an RBF Neural Network (RBFNN) that approximates a function. Since classification and function approximation problems are quite different, it is necessary to design a ne...

The Laplace equation that results from specifying either the normal or tangential force equilibrium equation in terms of the warping functions or its conjugate can be modeled as a complex variable boundary element method or CVBEM mixed boundary problem. The CVBEM is a well-known numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an...

We estimate the parameter of a stationary time series process by minimizing integrated weighted mean squared error between empirical and simulated characteristic function, when true functions cannot be explicitly computed. Motivated Indirect Inference, we use Monte Carlo approximation function based on i.i.d. blocks. As classical variance reduction technique, propose control variates for reduci...

In this paper we consider the problem of maximizing any submodular function subject to d knapsack constraints, where d is a fixed constant. We establish a strong relation between the discrete problem and its continuous relaxation, obtained through extension by expectation of the submodular function. Formally, we show that, for any non-negative submodular function, an α-approximation algorithm f...

In this paper, we propose a new multilevel univariate approximation method with high order accuracy using radial basis function interpolation and cubic B-spline quasi-interpolation. The proposed approach includes two schemes, which are based on radial basis function interpolation with less center points, and cubic B-spline quasi-interpolation operator. Error analysis shows that our method produ...