High relative accuracy with matrices of q-integers

被引：3
|
作者：
Delgado, Jorge [1 ]
Orera, Hector [1 ]
Pena, Juan M. [1 ]
机构：
[1] Univ Zaragoza, Dept Matemat Aplicada, Zaragoza, Spain
来源：
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2021年 / 28卷 / 05期
关键词：
bidiagonal decomposition; high relative accuracy; q‐ integers; quantum calculus; quantum orthogonal polynomials; total positivity;
D O I：
10.1002/nla.2383
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This article shows that the bidiagonal decomposition of many important matrices of q-integers can be constructed to high relative accuracy (HRA). This fact can be used to compute with HRA the eigenvalues, singular values, and inverses of these matrices. These results can be applied to collocation matrices of q-Laguerre polynomials, q-Pascal matrices, and matrices formed by q-Stirling numbers. Numerical examples illustrate the theoretical results.
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收藏
页数：20
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