We present a rigorous analysis of the primitive Gaussian basis sets used in the electronic structure theory. This leads to fundamental connections between Gaussian basis functions and the wavelet theory of multiresolution analysis. We also obtain a general description of basis set superposition error which holds for all localized, orthogonal or nonorthogonal, basis functions. The standard count...

The present paper is devoted to the development of a kind of spectral meshless radial point interpolation (SMRPI) technique in order to obtain a reliable approximate solution for buckling of nano-actuators subject to different nonlinear forces. To end this aim, a general type of the governing equation for nano-actuators, containing integro-differential terms and nonlinear forces is considered. ...

The paper describes the use of radial basis function neural networks with Gaussian basis functions to classify incomplete feature vectors. The method exploits the fact that any marginal distribution of a defined Gaussian joint distribution can be determined from the mean vector and covariance matrix of the joint distribution. The method is discussed in the context of complete and incomplete tra...

Radial basis function methods are modern ways to approximate multivariate functions, especially in the absence of grid data. They have been known, tested and analysed for several years now and many positive properties have been identified. This paper gives a selective but up-to-date survey of several recent developments that explains their usefulness from the theoretical point of view and contr...

In this addition to the regular paper, we derive the required derivatives required to implement the informative prior from a simulator in PILCO [1]. First, for completeness, we repeat the derivation of the mean, covariance, and input-output covariance of the predictive mean of a Gaussian process (GP) when the prior mean is a radial basis function network (RBF). Then, we detail the partial deriv...

For estimation of monthly precipitation, considering the intricacy and lack of accurate knowledge about the physical relationships, black box models usually are used because they produce more accurate values. In this article, a hybrid black box model, namely ANN-RBF, is proposed to estimate spatiotemporal value of monthly precipitation. In the first step a Multi Layer Perceptron (MLP) network i...

Radial basis function networks are usually trained according to a three-stage procedure. In the literature, many papers are devoted to the estimation of the position of Gaussian kernels, as well as the computation of the weights. Meanwhile, very few focus on the estimation of the kernel widths. In this paper, first, we develop a heuristic to optimize the widths in order to improve the generaliz...