Published October 6, 2015
| Submitted
Journal Article
Open
Smoothed analysis of symmetric random matrices with continuous distributions
- Creators
- Farrell, Brendan
- Vershynin, Roman
Abstract
We study invertibility of matrices of the form D + R, where D is an arbitrary symmetric deterministic matrix and is a symmetric random matrix whose independent entries have continuous distributions with bounded densities. We show that ||(D + R)^(-1)|| = O(n^2) with high probability. The bound is completely independent of D. No moment assumptions are placed on R; in particular the entries of R can be arbitrarily heavy-tailed.
Additional Information
© 2015 American Mathematical Society. Received by editor(s): September 26, 2014; Received by editor(s) in revised form: May 29, 2015; Published electronically: October 6, 2015. We thank the referees whose suggestions helped to improve the presentation of this paper. B. F. was partially supported by Joel A. Tropp under ONR awards N00014-08-1-0883 and N00014-11-1002 and a Sloan Research Fellowship. R. V. was partially supported by NSF grants 1001829, 1265782, and U. S. Air Force Grant FA9550-14-1-0009.Attached Files
Submitted - 1212.3531v3.pdf
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Additional details
- Eprint ID
- 65429
- Resolver ID
- CaltechAUTHORS:20160317-105140247
- N00014-08-1-0883
- Office of Naval Research (ONR)
- N00014-11-1002
- Office of Naval Research (ONR)
- Alfred P. Sloan Foundation
- 1001829
- NSF
- 1265782
- NSF
- FA9550-14-1-0009
- Air Force Office of Scientific Research (AFOSR)
- Created
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2016-03-17Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field