‎Radial basis functions (RBFs) are a powerful tool for approximating the solution of high-dimensional problems‎. ‎They are often referred to as a meshfree method and can be spectrally accurate‎. ‎In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the eigenfunction expansion‎. ‎We develop our approach in two-dimensional spaces for so...

Radial basis function (RBF) approximation is an extremely powerful tool for representing smooth functions in non-trivial geometries, since the method is meshfree and can be spectrally accurate. A perceived practical obstacle is that the interpolation matrix becomes increasingly illconditioned as the RBF shape parameter becomes small, corresponding to flat RBFs. Two stable approaches that overco...

This paper presents a novel approach for developing simulation metamodels using Gaussian radial basis functions. This approach is based on some recently developed mathematical results for radial basis functions. It is systematic, explicitly controls the underfitting and overfitting tradeoff, and uses a fast computational algorithm that requires minimal human involvement. This approach is illust...

Radial Basis Function Networks (RBFNs) have been successfully employed in several function approximation and pattern recognition problems. In RBFNs, radial basis functions are used to compute the activation of artificial neurons. The use of different radial basis functions in RBFN has been reported in the literature. Here, the use of the q-Gaussian function as a radial basis function in RBFNs i...

in this paper, an effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (rbfs). we present an algorithm based on interpolation by radial basis functions including multiquadratics (mqs), using legendre-gauss-lobatto nodes and weights. also a theorem is proved for convergence of the algorithm. some numerical examples are presented...

This paper establishes a direct method for solving variational problems via a set of Radial basis functions (RBFs) with Gauss-Chebyshev collocation centers. The method consist of reducing a variational problem into a mathematical programming problem. The authors use some optimization techniques to solve the reduced problem. Accuracy and stability of the multiquadric, Gaussian and inverse multiq...