计算Sturm-Liouville多项式的矩阵特征值法

IF 0.4 Q4 MATHEMATICS Missouri Journal of Mathematical Sciences Pub Date : 2022-05-01 DOI:10.35834/2022/3401019

F. Leibsle, N. Rhee, M. Bani-Yaghoub

{"title":"计算Sturm-Liouville多项式的矩阵特征值法","authors":"F. Leibsle, N. Rhee, M. Bani-Yaghoub","doi":"10.35834/2022/3401019","DOIUrl":null,"url":null,"abstract":"Summary: Recently the Legendre and other Sturm-Liouville (SL) polynomials were found as eigenvectors of certain matrices. However, the proposed algorithms are computationally incomplete and do not lead to general formulas to calculate the coeﬃcients of SL polynomials of any order. In this paper, we complete the algorithms based on a matrix-eigenvector method, which can be used to compute SL polynomials of any order. This includes Legendre, Hermite, Laguerre, and Chebyshev polynomials.","PeriodicalId":42784,"journal":{"name":"Missouri Journal of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Matrix-Eigenvalue Method to Compute Sturm-Liouville Polynomials\",\"authors\":\"F. Leibsle, N. Rhee, M. Bani-Yaghoub\",\"doi\":\"10.35834/2022/3401019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Summary: Recently the Legendre and other Sturm-Liouville (SL) polynomials were found as eigenvectors of certain matrices. However, the proposed algorithms are computationally incomplete and do not lead to general formulas to calculate the coeﬃcients of SL polynomials of any order. In this paper, we complete the algorithms based on a matrix-eigenvector method, which can be used to compute SL polynomials of any order. This includes Legendre, Hermite, Laguerre, and Chebyshev polynomials.\",\"PeriodicalId\":42784,\"journal\":{\"name\":\"Missouri Journal of Mathematical Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Missouri Journal of Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.35834/2022/3401019\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Missouri Journal of Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35834/2022/3401019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要：最近，勒让德多项式和其他斯特-刘维尔（SL）多项式被发现是某些矩阵的特征向量。然而，所提出的算法在计算上是不完整的，并且没有产生计算任何阶SL多项式系数的通用公式。在本文中，我们完成了基于矩阵特征向量方法的算法，该方法可用于计算任何阶的SL多项式。这包括勒让德多项式、埃尔米特多项式、拉盖尔多项式和切比雪夫多项式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

A Matrix-Eigenvalue Method to Compute Sturm-Liouville Polynomials

Summary: Recently the Legendre and other Sturm-Liouville (SL) polynomials were found as eigenvectors of certain matrices. However, the proposed algorithms are computationally incomplete and do not lead to general formulas to calculate the coeﬃcients of SL polynomials of any order. In this paper, we complete the algorithms based on a matrix-eigenvector method, which can be used to compute SL polynomials of any order. This includes Legendre, Hermite, Laguerre, and Chebyshev polynomials.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Missouri Journal of Mathematical Sciences MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： Missouri Journal of Mathematical Sciences (MJMS) publishes well-motivated original research articles as well as expository and survey articles of exceptional quality in mathematical sciences. A section of the MJMS is also devoted to interesting mathematical problems and solutions.

期刊最新文献

On Interval Valued fuzzy Bi-Quasi Ideals in Semigroups Generating the Group of Nonzero Elements Of a Quadratic Extension Of Fp $e^{*}$-Lifting Modules CHARACTERIZATION OF TRI-QUASI IDEALS AND THEIR FUZZIFICATIONS IN ORDERED SEMIRINGS A Diceless Game of the Classic and Finite Hyper Dice Backgammon: A New Class of Partizan Combinatorial Games