The smallest eigenvalue of large Hankel matrices

Mengkun Zhu, Yang Chen, Niall Emmart and Charles Weems

Applied Mathematics and Computation, 2018, vol. 334, issue C, 375-387

Abstract: We investigate the large N behavior of the smallest eigenvalue, λN, of an (N+1)×(N+1) Hankel (or moments) matrix HN, generated by the weight w(x)=xα(1−x)β,x∈[0,1],α>−1,β>−1. By applying the arguments of Szegö, Widom and Wilf, we establish the asymptotic formula for the orthonormal polynomials Pn(z),z∈C∖[0,1], associated with w(x), which are required in the determination of λN. Based on this formula, we produce the expressions for λN, for large N.

Keywords: Asymptotics; Smallest eigenvalue; Hankel matrices; Orthogonal polynomials; Parallel algorithm (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:334:y:2018:i:c:p:375-387

DOI: 10.1016/j.amc.2018.04.012

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