Continuously differentiable radial basis functions (C∞-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices full and can become very ill- conditioned. Similarly, Hilbert Vandermonde have ill-conditioned. The difference between a matrix generated by C∞-RBFs for partial differential or integral equations systems is t...

Elliptic boundary value problems (BVPs) are widely used in various scientific and engineering disciplines that involve finding solutions to elliptic partial differential equations subject certain conditions. This article introduces a novel approach for solving BVPs using an artificial neural network (ANN)-based radial basis function (RBF) collocation method. In this study, the backpropagation i...

In this paper, we present a numerical method for solving Hallen’s integral equation based on radial basis functions (RBFs). This method will represent the solution of Hallen’s integral equation by interpolating the radial basis functions based on Legendre-Gauss-Lobatto(LGL) nodes and weights. The numerical results show that the proposed method for Hallen’s integral equation is very accurate and...

Rates of approximation by networks with Gaussian RBFs with varying widths are investigated. For certain smooth functions, upper bounds are derived in terms of a Sobolev-equivalent norm. Coefficients involved are exponentially decreasing in the dimension. The estimates are proven using Bessel potentials as auxiliary approximating functions.

1. Briefly summarize the paper’s contributions. Does it address a new problem? Does it present a new approach? Does it show new types of results?  [AS] This paper presents a fast approach to reconstruct smooth, manifold surfaces from point clouds and to repair incomplete meshes using polyharmonic Radial Basis Functions (RBFs), which were previously thought to be too slow to compute to be scala...

Choosing the scale or shape parameter of radial basis functions (RBFs) is a well-documented but still an open problem in kernel-based methods. It common to tune it according applications, and plays crucial role both for accuracy stability method. In this paper, we first devise direct relation between RBFs their curvature at each point. This leads characterizing scalable unscalable ones. We prov...

Physical conservation laws are inherently Lagrangian. However, analyses in fluid mechanics using the Lagrangian framework often forgone favor of those Eulerian framework. This is perhaps due to a lack experimental techniques with high temporal and spatial resolution that track movement tracers flow domain. The development time-resolved Particle Tracking Velocimetry/Accelerometry (TR-PTV/A) meas...

A novel hybrid spectral method that combines radial basis function (RBF) and Chebyshev pseudospectral (PS) methods in a “2+1” approach is presented for numerically simulating thermal convection in a 3D spherical shell. This is the first study to apply RBFs to a full 3D physical model in spherical geometry. In addition to being spectrally accurate, RBFs are not defined in terms of any surface ba...

In a recent paper with Jerome we have suggested the use of a smoothing operation at each step of the basic multilevel approximation algorithm to improve the convergence rate of the algorithm. In our original paper the smoothing was deened via convolution, and its actual implementation was done via numerical quadrature. In this paper we suggest a diierent approach to smoothing, namely the use of...

This article is the third paper in a series aimed at establishment of authorship Russian-language texts. considers methods for determining classical Russian literary texts, as well fanfiction The process author was first considered version classification experiments using closed set authors, and were also completed complicated modification problem an open authors. use to identify text justified...