A fast procedure for the construction of quadrature formulas for bandlimited functions

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2023-09-01 DOI:10.1016/j.acha.2023.05.001

A. Gopal , V. Rokhlin

引用次数: 1

Abstract

We introduce an efficient scheme for the construction of quadrature rules for bandlimited functions. While the scheme is predominantly based on well-known facts about prolate spheroidal wave functions of order zero, it has the asymptotic CPU time estimate $O (n \log n)$ to construct an n-point quadrature rule. Moreover, the size of the “ $n \log n$ ” term in the CPU time estimate is small, so for all practical purposes the CPU time cost is proportional to n. The performance of the algorithm is illustrated by several numerical examples.

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一个快速构造带限函数的正交公式的程序

我们介绍了一种构造带限函数求积规则的有效方案。虽然该方案主要基于关于零阶椭球波函数的众所周知的事实，但它具有渐近CPU时间估计O（nlog⁡n）以构造n点求积规则。此外，“nlog”的大小⁡CPU时间估计中的“n”项很小，因此出于所有实际目的，CPU时间成本与n成正比。通过几个数值示例说明了算法的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.