Related papers: Approximation of a Multivariate Function of Bounde…
This paper studies the influence of scaling on the behavior of Radial Basis Function interpolation. It focuses on certain central aspects, but does not try to be exhaustive. The most important questions are: How does the error of a…
Researchers have been persistently working to address the issue of missing values in time series data. Numerous models have been proposed, striving to estimate the distribution of the data. The Radial Basis Functions Neural Network (RBFNN)…
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system which is called fractal interpolation function. We generalize the notion of fractal…
This paper aims to survey our recent work relating to the radial basis function (RBF) from some new views of points. In the first part, we established the RBF on numerical integration analysis based on an intrinsic relationship between the…
We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce…
A novel approach to zipper fractal interpolation theory for functions of several variables is proposed. We develop multivariate zipper fractal functions in a constructive manner. We then perturb a multivariate function to construct its…
In this paper, we present a spectral method based on Radial Basis Functions (RBFs) for numerically solving the fully nonlinear 1D Serre Green-Naghdi equations. The approximation uses an RBF discretization in space and finite differences in…
Basis Function (BF) expansions are a cornerstone of any engineer's toolbox for computational function approximation which shares connections with both neural networks and Gaussian processes. Even though BF expansions are an intuitive and…
In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial…
Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…
In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation…
This paper addresses the problem of accurately estimating a function on one domain when only its discrete samples are available on another domain. To answer this challenge, we utilize a neural network, which we train to incorporate prior…
We study algorithms to estimate geometric properties of raw point cloud data through implicit surface representations. Given that any level-set function with a constant level set corresponding to the surface can be used for such…
In this paper we obtain approximated numerical solutions for the 2D Helmholtz equation using a radial basis function-generated finite difference scheme (RBF-FD), where weights are calculated by applying an oscillatory radial basis function…
Radial basis function generated finite difference (RBF-FD) methods for PDEs require a set of interpolation points which conform to the computational domain $\Omega$. One of the requirements leading to approximation robustness is to place…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
Here we research the univariate quantitative approximation of real and complex valued continuous functions on a compact interval or all the real line by quasi-interpolation, Baskakov type and quadrature type neural network operators. We…
Because physical phenomena on Earth's surface occur on many different length scales, it makes sense when seeking an efficient approximation to start with a crude global approximation, and then make a sequence of corrections on finer and…
Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate…
This note establishes a theoretical framework for finding (potentially overparameterized) approximations of a function on a compact set with a-priori bounds for the generalization error. The approximation method considered is to choose,…