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The smallest eigenvalue of large Hankel matrices
Zhu, Mengkun1; Chen, Yang1; Emmart, Niall2; Weems, Charles2
2018-10
Source PublicationAPPLIED MATHEMATICS AND COMPUTATION
ISSN0096-3003
Volume334Pages:375-387
Abstract

We investigate the large N behavior of the smallest eigenvalue, lambda(N), of an (N + 1) x ( N + 1) Hankel (or moments) matrix H-N, generated by the weight w(x) = x(alpha)(1 - x)(beta), x is an element of [0, 1], alpha > 1, beta > 1. By applying the arguments of Szego, Widom and Wilf, we establish the asymptotic formula for the orthonormal polynomials P-n(z), z is an element of C \ [0, 1], associated with w(x), which are required in the determination of lambda(N). Based on this formula, we produce the expressions for lambda(N), for large N.

KeywordAsymptotics Smallest Eigenvalue Hankel Matrices Orthogonal Polynomials Parallel Algorithm
DOIhttp://doi.org/10.1016/j.amc.2018.04.012
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000432790300028
PublisherELSEVIER SCIENCE INC
The Source to ArticleWOS
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Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorChen, Yang
Affiliation1.Department of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, China
2.College of Information and Computer Sciences, University of Massachusetts, Amherst, MA 01003, USA
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Zhu, Mengkun,Chen, Yang,Emmart, Niall,et al. The smallest eigenvalue of large Hankel matrices[J]. APPLIED MATHEMATICS AND COMPUTATION,2018,334:375-387.
APA Zhu, Mengkun,Chen, Yang,Emmart, Niall,&Weems, Charles.(2018).The smallest eigenvalue of large Hankel matrices.APPLIED MATHEMATICS AND COMPUTATION,334,375-387.
MLA Zhu, Mengkun,et al."The smallest eigenvalue of large Hankel matrices".APPLIED MATHEMATICS AND COMPUTATION 334(2018):375-387.
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