标量Wiener-Hopf方程近似解的一种构造方法
A Constructive Method for Approximate Solution to Scalar Wiener-Hopf Equations
AI总结：
本文提出一种基于有理Carathéodory-Fejér近似的标量Wiener-Hopf方程近似求解方法，具有可靠性高、误差界明确且多项式次数低等优点。
摘要：
本文提出了一种近似标量Wiener-Hopf方程的新方法，并由此构造近似解。与现有方法相比，该方法的优势在于可靠性和显式误差界。此外，有理逼近中多项式的次数远低于其他方法。数值解的需求源于精确解计算的困难。本文发展的近似方法旨在推广到矩阵Wiener-Hopf方程，其精确解通常未知。论文第一部分建立了对于1<p<∞的Lp误差界，这些误差界表明了方程逼近的精度如何决定解的逼近精度。第二部分描述了采用有理Carathéodory-Fejér逼近近似求解Wiener-Hopf方程的方法。该方法通过构造实直线到单位区间的映射进行适配。文中包含了使用所提技术的数值示例（在Chebfun上执行），在整个实直线上误差小至10^{-12}。
英文摘要：
This paper presents a novel method of approximating the scalar Wiener-Hopf equation; and therefore constructing an approximate solution. The advantages of this method over the existing methods are reliability and explicit error bounds. Additionally the degrees of the polynomials in the rational approximation are considerably smaller than in other approaches. The need for a numerical solution is motivated by difficulties in computation of the exact solution. The approximation developed in this paper is with a view of generalisation to matrix Wiener-Hopf for which the exact solution, in general, is not known. The first part of the paper develops error bounds in Lp for 1<p<\infty. These indicate how accurately the solution is approximated in terms of how accurate the equation is approximated. The second part of the paper describes the approach of approximately solving the Wiener-Hopf equation that employs the Rational Caratheodory-Fejer Approximation. The method is adapted by constructing a mapping of the real line to the unit interval. Numerical examples to demonstrate the use of the proposed technique are included (performed on Chebfun), yielding error as small as 10^{-12} on the whole real line.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
