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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 109, 22 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.109
(Mi sigma1191)
 

This article is cited in 2 scientific papers (total in 2 papers)

Smoothed Analysis for the Conjugate Gradient Algorithm

Govind Menona, Thomas Trogdonb

a Division of Applied Mathematics, Brown University, 182 George St., Providence, RI 02912, USA
b Department of Mathematics, University of California, Irvine, Rowland Hall, Irvine, CA, 92697-3875, USA
Full-text PDF (966 kB) Citations (2)
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Abstract: The purpose of this paper is to establish bounds on the rate of convergence of the conjugate gradient algorithm when the underlying matrix is a random positive definite perturbation of a deterministic positive definite matrix. We estimate all finite moments of a natural halting time when the random perturbation is drawn from the Laguerre unitary ensemble in a critical scaling regime explored in Deift et al. (2016). These estimates are used to analyze the expected iteration count in the framework of smoothed analysis, introduced by Spielman and Teng (2001). The rigorous results are compared with numerical calculations in several cases of interest.
Keywords: conjugate gradient algorithm; Wishart ensemble; Laguerre unitary ensemble; smoothed analysis.
Funding agency Grant number
National Science Foundation DMS-1411278
DMS-1303018
This work was supported in part by grants NSF-DMS-1411278 (GM) and NSF-DMS-1303018 (TT).
Received: May 23, 2016; in final form October 31, 2016; Published online November 6, 2016
Bibliographic databases:
Document Type: Article
MSC: 60B20; 65C50; 35Q15
Language: English
Citation: Govind Menon, Thomas Trogdon, “Smoothed Analysis for the Conjugate Gradient Algorithm”, SIGMA, 12 (2016), 109, 22 pp.
Citation in format AMSBIB
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\paper Smoothed Analysis for the Conjugate Gradient Algorithm
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\vol 12
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\totalpages 22
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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