Computation of pairs of related Gauss-type quadrature rules

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI:10.1016/j.apnum.2024.03.003

H. Alqahtani , C.F. Borges , D.Lj. Djukić , R.M. Mutavdžić Djukić , L. Reichel , M.M. Spalević

引用次数: 0

Abstract

The evaluation of Gauss-type quadrature rules is an important topic in scientific computing. To determine estimates or bounds for the quadrature error of a Gauss rule often another related quadrature rule is evaluated, such as an associated Gauss-Radau or Gauss-Lobatto rule, an anti-Gauss rule, an averaged rule, an optimal averaged rule, or a Gauss-Kronrod rule when the latter exists. We discuss how pairs of a Gauss rule and a related Gauss-type quadrature rule can be computed efficiently by a divide-and-conquer method.

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计算成对相关的高斯型正交规则

高斯正交规则的评估是科学计算中的一个重要课题。为了确定高斯规则正交误差的估计值或界限，通常要评估另一个相关的正交规则，如相关的高斯-拉道规则或高斯-洛巴图规则、反高斯规则、平均规则、最优平均规则或高斯-克朗罗德规则（如果存在后者）。我们将讨论如何通过分而治之的方法高效计算高斯规则和相关的高斯型正交规则对。

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 Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.