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Licensed Unlicensed Requires Authentication Published by De Gruyter July 12, 2018

Rayleigh Quotient Methods for Estimating Common Roots of Noisy Univariate Polynomials

  • Alwin Stegeman and Lieven De Lathauwer ORCID logo EMAIL logo

Abstract

The problem is considered of approximately solving a system of univariate polynomials with one or more common roots and its coefficients corrupted by noise. The goal is to estimate the underlying common roots from the noisy system. Symbolic algebra methods are not suitable for this. New Rayleigh quotient methods are proposed and evaluated for estimating the common roots. Using tensor algebra, reasonable starting values for the Rayleigh quotient methods can be computed. The new methods are compared to Gauss–Newton, solving an eigenvalue problem obtained from the generalized Sylvester matrix, and finding a cluster among the roots of all polynomials. In a simulation study it is shown that Gauss–Newton and a new Rayleigh quotient method perform best, where the latter is more accurate when other roots than the true common roots are close together.

MSC 2010: 13P15; 15A18; 65F15

Award Identifier / Grant number: G0F6718N

Funding statement: Research supported by (1) Research Council KU Leuven: C1 project c16/15/059-nD and (2) FWO: EOS project G0F6718N (SELMA).

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Received: 2017-08-31
Revised: 2018-03-06
Accepted: 2018-05-02
Published Online: 2018-07-12
Published in Print: 2019-01-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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