Related papers: Multiple-location matched approximation for Bessel…
A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates…
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…
We introduce another new type of combinations of Bernstein operators in this paper, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type…
The Bessel-Neumann expansion (of integer order) of a function $g:\mathbb{C}\rightarrow\mathbb{C}$ corresponds to representing $g$ as a linear combination of basis functions $\phi_0,\phi_1,\ldots$, i.e., $g(z)=\sum_{\ell = 0}^\infty w_\ell…
A fundamental solution of Laplace's equation in three dimensions is expanded in harmonic functions that are separated in parabolic or elliptic cylinder coordinates. There are two expansions in each case which reduce to expansions of the…
This is the first installment in a series of papers devoted to examining certain aspects of the asymptotic value distribution and distribution of zeros manifested by members of a broad class of linear combinations of L-functions in the…
This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to construct basis functions that have optimal local…
Linear combinations of translations of a single Gaussian, e^{-x^2}, are shown to be dense in L^2(R). Two algorithms for determining the coefficients for the approximations are given, using orthogonal Hermite functions and least squares.…
The aim of this work is to study new functions arising from the limit transition of the Jackson's $q$-Bessel functions when $q\rightarrow -1$. These functions coincide with the $cas$ function for particular values of their parameters. We…
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
From new integral representations of the $n$-th derivative of Bessel functions with respect to the order, we derive some reflection formulas for the first and second order derivative of $J_{\nu }\left( t\right) $ and $% Y_{\nu }\left(…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
Graph-based approximation methods are of growing interest in many areas, including transportation, biological and chemical networks, financial models, image processing, network flows, and more. In these applications, often a basis for the…
Radial basis functions have become a popular tool for approximation and solution of partial differential equations (PDEs). The recently proposed multilevel sparse interpolation with kernels (MuSIK) algorithm proposed in \cite{Georgoulis}…
A Green's function based solver for the modified Bessel equation has been developed with the primary motivation of solving the Poisson equation in cylindrical geometries. The method is implemented using a Discrete Hankel Transform and a…
The tree-level three-point correlation functions of local operators in the general $(p,q)$ minimal models coupled to gravity are calculated in the continuum approach. On one hand, the result agrees with the unitary series ($q=p+1$); and on…
We give direct and inverse theorems for the weighted approximation of functions with endpoint singularities by combinations of Bernstein operators.
We present a dimension-incremental algorithm for the nonlinear approximation of high-dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to detect a suitable truncation of the basis expansion of the…
We recently proposed a general algorithm for approximating nonstandard Bayesian posterior distributions by minimization of their Kullback-Leibler divergence with respect to a more convenient approximating distribution. In this note we offer…
We study multivariate integration and approximation for functions belonging to a weighted reproducing kernel Hilbert space based on half-period cosine functions in the worst-case setting. The weights in the norm of the function space depend…