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A comprehensive perturbation theorem for estimating magnitudes of roots of polynomials

Published online by Cambridge University Press:  14 February 2013

M. Pakdemirli  and
G. Sarı
M. Pakdemirli
Affiliation:
Applied Mathematics & Computation Center, Department of Mechanical Engineering, Celal Bayar University, 45140, Muradiye, Manisa, Turkey email [email protected]
G. Sarı
Affiliation:
Applied Mathematics & Computation Center, Department of Mechanical Engineering, Celal Bayar University, 45140, Muradiye, Manisa, Turkey email [email protected]

Abstract

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A comprehensive new perturbation theorem is posed and proven to estimate the magnitudes of roots of polynomials. The theorem successfully determines the magnitudes of roots for arbitrary degree of polynomial equations with no restrictions on the coefficients. In the previous papers ‘Pakdemirli and Elmas, Appl. Math. Comput. 216 (2010) 1645–1651’ and ‘Pakdemirli and Yurtsever, Appl. Math. Comput. 188 (2007) 2025–2028’, the given theorems were valid only for some restricted coefficients. The given theorem in this work is a generalization and unification of the past theorems and valid for arbitrary coefficients. Numerical applications of the theorem are presented as examples. It is shown that the theorem produces good estimates for the magnitudes of roots of polynomial equations of arbitrary order and unrestricted coefficients.

Keywords

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 16 , October 2013 , pp. 1 - 8
Copyright
© The Author(s) 2013 

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