具有多项式系数的特殊二阶线性回归方程解的渐近性和多项式滤波器的边界效应

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Symbolic Computation Pub Date : 2024-09-26 DOI:10.1016/j.jsc.2024.102386

Alexey A. Kytmanov , Sergey P. Tsarev

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引用次数: 0

摘要

在本文中，我们证明了经典的高次离散正交多项式（等距网格上的哈恩多项式，具有单位权重）在端点附近具有极小的值（我们称这一特性为 "端点附近快速衰减"），但在这些网格点和它们的根非常靠近端点附近的网格点之间具有极大的值。这些结果意味着稳定的线性多项式滤波器具有重要的一般边界效应（我们称这一特性为 "快速边界衰减"）。我们的结果给出了 M.Petkovšek 所研究的具有多项式系数的特殊二阶线性递归的实际重要解的非难渐近的有趣例子；我们将本文献给他。

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Asymptotics of solutions of special second-order linear recurrencies with polynomial coefficients and boundary effects of polynomial filters

In this paper we prove that classical discrete orthogonal polynomials (Hahn polynomials on an equidistant grid with unit weights) of high degrees have extremely small values near the endpoints (we call this property “rapid decay near the endpoints”) but extremely large values between these grid points and their roots are very close to the grid points near the endpoints. These results imply important general boundary effects for stable linear polynomial filters (we call this property “rapid boundary attenuation”).

Our results give interesting examples of nontrivial asymptotics of practically important solutions of special second-order linear recurrencies with polynomial coefficients studied by M.Petkovšek; to his memory we dedicate this paper.

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来源期刊

Journal of Symbolic Computation 工程技术-计算机：理论方法

CiteScore

2.10

自引率

14.30%

发文量

审稿时长

142 days

期刊介绍： An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects. It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.