线性微分方程解的Chebyshev展开式
Chebyshev Expansions for Solutions of Linear Differential Equations
摘要：
切比雪夫展开式是以第一类切比雪夫多项式为基础的级数。当这样的级数解线性微分方程时，其系数满足线性递归方程。我们解释这个方程作为一个分数的线性递归算子的分子。这种解释使我们能够简单地了解以前的算法，分析它们的复杂性，并设计一个更快的大订单。
英文摘要：
A Chebyshev expansion is a series in the basis of Chebyshev polynomials of the first kind. When such a series solves a linear differential equation, its coefficients satisfy a linear recurrence equation. We interpret this equation as the numerator of a fraction of linear recurrence operators. This interpretation lets us give a simple view of previous algorithms, analyze their complexity, and design a faster one for large orders.
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。
