PUMA
Istituto di Informatica e Telematica     
Del Corso G., Manzini G. On the Randomized Error of Polynomial Methods for Eigenvector and Eigenvalue Estimate. Technical report, 1999.
 
 
Abstract
(English)
In this paper we consider the problem of estimating the largest eigenvalue and the corresponding eigenvector of a symmetric matrix. In particular, we consider iterative methods, such as the power method and Lanczos algorithm. These methods need a starting vector which is usually chosen randomly. We analyze the behavior of these methods when the initial vector is chosen with uniform distribution over the unit n-dimensional sphere. In particular, we give upper and lower bounds on the L_p norm of the randomized error, and we improve previously known bounds with a detailed analysis of the role of the multiplicity of the largest eigenvalue.
Subject Power and Lanczos methods
Eigenvalues and eigenvectors
Random start
Randomized error



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