Reinforcement learning (RL) is a machine learning technique for sequential decision making. This approach is well proven in many small-scale domains. The true potential of this technique cannot be fully realised until it can adequately deal with the large domain sizes that typically describe real world problems. RL with function approximation is one method of dealing with the domain size proble...

This article shows a relationship between two different approximation techniques: the support vector machines (SVM), proposed by V. Vapnik (1995) and a sparse approximation scheme that resembles the basis pursuit denoising algorithm (Chen, 1995; Chen, Donoho, and Saunders, 1995). SVM is a technique that can be derived from the structural risk minimization principle (Vapnik, 1982) and can be use...

 This paper presents the tunable technique of the analog filter at high frequency fp = 1 MHz by used the Fractional-order   n   step, where n is an original of integerorder on circuit and  is an approximation order step 0 1    , An approximation order is designed from the Fractance circuits, and also presents the approximation function of the Fractional-order Laplacian s  design on th...

Interpolation by translates of \radial" basis functions is optimal in the sense that it minimizes the pointwise error functional among all comparable quasi{interpolants on a certain \native" space of functions F . Since these spaces are rather small for cases where is smooth, we study the behavior of interpolants on larger spaces of the form F 0 for less smooth functions 0. It turns out that in...

This paper gives an introduction to certain techniques for the construction of geometric objects from scattered data. Special emphasis is put on interpolation methods using compactly supported radial basis functions. x1. Introduction We assume a sample of multivariate scattered data to be given as a set X = solid to these data will be the range of a smooth function s : IR d ! IR D with s(x k) =...

Having various concrete industrial applications in mind we focus on surface fitting to large scattered data sets. We describe a general method for modelling data which incorporates both filtering using triangulations, and hierarchical interpolation based on compactly supported radial basis functions. The uniformity of the data points plays a significant role. The utility of the method is confir...

This contribution will touch the following topics: Short introduction into the theory of multivariate interpolation and approximation by nitely many (irregular) translates of a (not necessarily radial) basis function, motivated by optimal recovery of functions from discrete samples. Native spaces of functions associated to conditionally positive definite functions, and relations between such sp...

We prove that the well known Lp-error estimates for radial basis function interpolation are optimal provided that the underlying function space is the native Hilbert space of the basis function. Furthermore we give upper bounds for the approximation orders in case of best L1-approximation using radial basis functions.

We discuss the problem of constrained approximation and interpolation of scattered data by using compactly supported radial basis functions, subjected to the constraint of preserving positivity. The approaches are presented to compute positive approximation and interpolation by solving the two corresponding optimization problems. Numerical experiments are provided to illustrate that the propose...

⎯ This paper presents the tunable technique of the analog filter at high frequency fp = 1 MHz by used the Fractional-order ( ) n α + step, where n is an original of integerorder on circuit and α is an approximation order step 0 1 α < < , An approximation order is designed from the Fractance circuits, and also presents the approximation function of the Fractional-order Laplacian sα design on the...