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The smallest eigenvalue of large Hankel matrices
Zhu, Mengkun1; Chen, Yang1; Emmart, Niall2; Weems, Charles2

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
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WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000432790300028
The Source to ArticleWOS
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
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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