A MATRIX-EIGENVALUE METHOD TO COMPUTE STURM-LIOUVILLE POLYNOMIALS

被引：0

作者：

Leibsle, Fred M. ^{[1
]}

Rhee, Noah ^{[2
]}

Bani-Yaghoub, Majid ^{[2
]}

机构：

[1] Univ Missouri, Dept Phys & Astron, 5110 Rockhill Rd, Kansas City, MO 64110 USA

[2] Univ Missouri, Dept Math & Stat, 5110 Rockhill Rd, Kansas City, MO 64110 USA

来源：

MISSOURI JOURNAL OF MATHEMATICAL SCIENCES | 2022年 / 34卷 / 01期

关键词：

Sturm-Liouville Equations; Self-Adjoint Operators; Eigenvalues; Eigenvectors; Upper Triangular Matrices; Back-Substitution; DIFFERENTIAL-EQUATIONS;

D O I：

10.35834/2022/3401019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Recently the Legendre and other Sturm-Liouville (SL) polynomials were found as eigenvectors of certain matrices [2, 3, 4, 5]. 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.

引用

页码：19 / 29

页数：11

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