{"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}
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.
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.