Related papers: A Radial Basis Function Approximation for Large Da…
We propose a novel framework for solving nonlinear PDEs using sparse radial basis function (RBF) networks. Sparsity-promoting regularization is employed to prevent over-parameterization and reduce redundant features. This work is motivated…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…
The Hermite radial basis functions (HRBFs) implicits have been used to reconstruct surfaces from scattered Hermite data points. In this work, we propose a closed-form formulation to construct HRBF-based implicits by a quasi-solution…
Boundary value problems on the unit sphere arise naturally in geophysics and oceanography when scientists model a physical quantity on large scales. Robust numerical methods play an important role in solving these problems. In this article,…
When solving partial differential equations on scattered nodes using the Radial Basis Function generated Finite Difference (RBF-FD) method, one of the parameters that must be chosen is the stencil size. Focusing on Polyharmonic Spline RBFs…
The aim of this paper is to solve numerically, using the meshless method via radial basis functions, time-space-fractional partial differential equations of type Black-Scholes. The time-fractional partial differential equation appears in…
We introduce an adaptive scattered data fitting scheme as extension of local least squares approximations to hierarchical spline spaces. To efficiently deal with non-trivial data configurations, the local solutions are described in terms of…
We analyze the approximation by radial basis functions of a hypersingular integral equation on an open surface. In order to accommodate the homogeneous essential boundary condition along the surface boundary, scaled radial basis functions…
Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…
In this study,a new method was presented by developing Reduced differential transform method in order to find approximate solution of partial differential equations. Here, RDTM with fixed grid size algorithm was developed for the first time…
Recently, collocation based radial basis function (RBF) partition of unity methods (PUM) for solving partial differential equations have been formulated and investigated numerically and theoretically. When combined with stable evaluation…
Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…
In solving the variational problem, the key is to efficiently find the target function that minimizes or maximizes the specified functional. In this paper, by using the Pade approximant, we suggest a methods for the variational problem. By…
We propose a method to approximate the distribution of robot configurations satisfying multiple objectives. Our approach uses variational inference, a popular method in Bayesian computation, which has several advantages over sampling-based…
Density Functional Theory calculations traditionally suffer from an inherent cubic scaling with respect to the size of the system, making big calculations extremely expensive. This cubic scaling can be avoided by the use of so-called linear…
Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding…
The definitions and applications of Radial Distribution Function (RDF) and Structure Factor (SF) to study properties of aggregate are found in many papers and books. The approach adopted to calculate the RDF and the SF to determine the…
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…