In this paper, we study the statistical properties of method of regularization with radial basis functions in the context of linear inverse problems. Radial basis function regularization is widely used in machine learning because of its demonstrated effectiveness in numerous applications and computational advantages. From a statistical viewpoint, one of the main advantages of radial basis funct...

soil alkalinity and salinity are serious problems in arid and semi-arid regions, and therefore monitoring of soil ph and electrical conductivity (ec) is necessary in any region. the present study aimed to properly interpolate soil ph and ec as soil quality indices in a semi-arid mountainous area with annual precipitation of 342.4 mm. the study area is the karimabad rangelands in hamadan provinc...

ii Preface Radial Basis Function (RBF) methods have become the primary tool for interpolating multidimensional scattered data. RBF methods also have become important tools for solving Partial Differential Equations (PDEs) in complexly shaped domains. Classical methods for the numerical solution of PDEs (finite difference, finite element, finite volume, and pseudospectral methods) are based on p...

The average diffusion propagator (ADP) obtained from diffusion MRI (dMRI) data encapsulates important structural properties of the underlying tissue. Measures derived from the ADP can be potentially used as markers of tissue integrity in characterizing several mental disorders. Thus, accurate estimation of the ADP is imperative for its use in neuroimaging studies. In this work, we propose a sim...

In a motorized spindle, due to the complexity of the system and nonlinear relationship between features and types of faults, it is difficult and inefficient to use traditional methods or physical models for the fault diagnosis. This paper focuses on the research on applying Radial Basis Function (RBF) Networks for fault detection and classification in the motorized spindle. As a data driven mod...

A review of interpolation to values of a function f(x), x 2 R d , by radial basis function methods is given. It addresses the nonsingularity of the interpolation equations, the inclusion of polynomial terms, and the accuracy of the approximation sf, where s is the interpolant. Then some numerical experiments investigate the situation when the data points are on a low dimensional nonlinear manif...

This paper presents mesh-free procedures for solving linear differential equations (ODEs and elliptic PDEs) based on multiquadric (MQ) radial basis function networks (RBFNs). Based on our study of approximation of function and its derivatives using RBFNs that was reported in an earlier paper (Mai-Duy, N. & Tran-Cong, T. (1999). Approximation of function and its derivatives using radial basis fu...

A treecode is presented for evaluating sums defined in terms of the multiquadric radial basis function (RBF), φ(x) = (|x|2 + c2)1/2, where x ∈ R3 and c ≥ 0. Given a set of N nodes, evaluating an RBF sum directly requires CPU time that scales like O(N2). For a given level of accuracy, the treecode reduces the CPU time to O(N logN) using a far-field expansion of φ(x). We consider two options for ...