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Published August 2006 | Version Submitted
Journal Article Open

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

Creators

  • 1. ROR icon King's College London
  • 2. ROR icon California Institute of Technology

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.

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.

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Submitted - 0603098.pdf

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Additional details

Identifiers

Eprint ID
77387
Resolver ID
CaltechAUTHORS:20170512-073744225

Related works

Describes
https://arxiv.org/abs/math/0603098 (URL)

Funding

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

Dates

Created
2017-05-12
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Updated
2021-11-15
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Caltech groups
Mathematics Department , Physics Department