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A Method of Order 1+SQRT(3) for Computing the Smallest Eigenvalue of a Symmetric Toeplitz Matrix

descriptionPublicationkeyboard_double_arrow_right External research report , Other literature type 01 Jan 2002Embargo end date: 27 Feb 2006 English Publisher:TUHH Universitätsbibliothek
Authors: Kostić, Aleksandra; Voß, Heinrich;

doi: 10.15480/882.160

A Method of Order 1+SQRT(3) for Computing the Smallest Eigenvalue of a Symmetric Toeplitz Matrix

Abstract

In this note we discuss a method of order 1+sqrt(3) for computing the smallest eigenvalue lambda_1 of a symmetric and positive definite Toeplitz matrix. It generalizes and improves a method introduced in cite{MacVos97} which is based on rational Hermitean interpolation of the secular equation. Taking advantage of a further rational approximation of the secular equation which is essentially for free and which yields lower bounds of lambda_1 we obtain an improved stopping criterion.

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Keywords

Eigenwertproblem, Mathematik, Toeplitz-Matrix, secular equation, eigenvalue problem, Toeplitz matrix, Eigenvalues, eigenvectors

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
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