Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle

Davies, E. B. and Simon, B. (2006) Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle. Journal of Approximation Theory, 141 (2). pp. 189-213. ISSN 0021-9045. doi:10.1016/j.jat.2006.03.006. https://resolver.caltech.edu/CaltechAUTHORS:20170512-073744225

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Abstract

We prove that for any n×n matrix, A, and z with |z|⩾∥A∥, we have that ∥(z-A)^(-1) ∥⩽cot(^π_(4n))dist(z,spec(A))^(-1). We apply this result to the study of random orthogonal polynomials on the unit circle.

Item Type:

Article

Related URLs:

URL	URL Type	Description
https://doi.org/10.1016/j.jat.2006.03.006	DOI	Article
http://www.sciencedirect.com/science/article/pii/S0021904506000487	Publisher	Article
https://arxiv.org/abs/math/0603098	arXiv	Discussion Paper

ORCID:

Author	ORCID
Simon, B.	0000-0003-2561-8539

Additional Information:

© 2006 Elsevier Inc. Received 30 August 2005, Accepted 3 March 2006, Available online 15 May 2006. Communicated by Paul Nevai Supported in part by EPSRC grant GR/R81756. Supported in part by NSF grant DMS-0140592. This work was done while B. Simon was a visitor at King’s College London. He would like to thank A.N. Pressley and E.B. Davies for the hospitality of King’s College, and the London Mathematical Society for partial support. The calculations of M. Stoiciu [20,21] were an inspiration for our pursuing the estimate we found. We appreciate useful correspondence/discussions with M. Haase, N. Higham, R. Nagel, N.K. Nikolski, V. Totik, and L.N. Trefethen.

Funders:

Funding Agency	Grant Number
Engineering and Physical Sciences Research Council (EPSRC)	GR/R81756
NSF	DMS-0140592

Issue or Number:

DOI:

10.1016/j.jat.2006.03.006

Record Number:

CaltechAUTHORS:20170512-073744225

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20170512-073744225

Official Citation:

E.B. Davies, B. Simon, Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle, Journal of Approximation Theory, Volume 141, Issue 2, 2006, Pages 189-213, ISSN 0021-9045, http://dx.doi.org/10.1016/j.jat.2006.03.006. (http://www.sciencedirect.com/science/article/pii/S0021904506000487)

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ID Code:

77387

Collection:

CaltechAUTHORS

Deposited By:

Ruth Sustaita

Deposited On:

12 May 2017 23:54

Last Modified:

15 Nov 2021 17:30

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