Published August 2006
| Submitted
Journal Article
Open
Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle
- Creators
- Davies, E. B.
-
Simon, B.
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.Attached Files
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Additional details
- Eprint ID
- 77387
- Resolver ID
- CaltechAUTHORS:20170512-073744225
- GR/R81756
- Engineering and Physical Sciences Research Council (EPSRC)
- DMS-0140592
- NSF
- Created
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2017-05-12Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field