ﻻ يوجد ملخص باللغة العربية
We present a fast method for evaluating expressions of the form $$ u_j = sum_{i = 1,i ot = j}^n frac{alpha_i}{x_i - x_j}, quad text{for} quad j = 1,ldots,n, $$ where $alpha_i$ are real numbers, and $x_i$ are points in a compact interval of $mathbb{R}$. This expression can be viewed as representing the electrostatic potential generated by charges on a line in $mathbb{R}^3$. While fast algorithms for computing the electrostatic potential of general distributions of charges in $mathbb{R}^3$ exist, in a number of situations in computational physics it is useful to have a simple and extremely fast method for evaluating the potential of charges on a line; we present such a method in this paper, and report numerical results for several examples.
We present a new fast algorithm for computing the Boys function using nonlinear approximation of the integrand via exponentials. The resulting algorithms evaluate the Boys function with real and complex valued arguments and are competitive with previously developed algorithms for the same purpose.
Developments of nonlocal operators for modeling processes that traditionally have been described by local differential operators have been increasingly active during the last few years. One example is peridynamics for brittle materials and another is
The Cadzows algorithm is a signal denoising and recovery method which was designed for signals corresponding to low rank Hankel matrices. In this paper we first introduce a Fast Cadzows algorithm which is developed by incorporating a novel subspace p
The paper is concerned with the three-dimensional electromagnetic scattering from a large open rectangular cavity that is embedded in a perfectly electrically conducting infinite ground plane. By introducing a transparent boundary condition, the scat
In this article, we devise a concise algorithm for computing BOCP. Our method is simple, easy-to-implement but without loss of efficiency. Given two circular-arc polygons with $m$ and $n$ edges respectively, our method runs in $O(m+n+(l+k)log l)$ tim