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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. 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:
URLURL TypeDescription
https://doi.org/10.1016/j.jat.2006.03.006DOIArticle
http://www.sciencedirect.com/science/article/pii/S0021904506000487PublisherArticle
https://arxiv.org/abs/math/0603098arXivDiscussion Paper
ORCID:
AuthorORCID
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 AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)GR/R81756
NSFDMS-0140592
Issue or Number:2
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)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77387
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:12 May 2017 23:54
Last Modified:03 Oct 2019 17:57

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