Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T22:55:58.044Z Has data issue: false hasContentIssue false
  • English
  • Français

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 mpak@cbu.edu.tr
G. Sarı
Affiliation:
Applied Mathematics & Computation Center, Department of Mechanical Engineering, Celal Bayar University, 45140, Muradiye, Manisa, Turkey email gozde.deger@cbu.edu.tr

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 

References

Abbasbandy, S., ‘Improving Newton–Raphson method for nonlinear equations by modified Adomian decomposition method’, Appl. Math. Comput. 145 (2003) 887–893.Google Scholar
Hinch, E. J., Perturbation methods (Cambridge University Press, New York, 1991).Google Scholar
Householder, A. S., The numerical treatment of a single nonlinear equation (McGraw-Hill, New York, 1970).Google Scholar
Nayfeh, A. H., Introduction to perturbation techniques (John Wiley and Sons, New York, 1981).Google Scholar
Pakdemirli, M. and Boyacı, H., ‘Generation of root finding algorithms via perturbation theory and some formulas’, Appl. Math. Comput. 184 (2007) 783–788.Google Scholar
Pakdemirli, M., Boyacı, H. and Yurtsever, H. A., ‘Perturbative derivation and comparisons of root-finding algorithms with fourth order derivatives’, Math. Comput. Appl. 12 (2007) 117–124.Google Scholar
Pakdemirli, M., Boyacı, H. and Yurtsever, H. A., ‘A root-finding algorithm with fifth order derivatives’, Math. Comput. Appl. 13 (2008) 123–128.Google Scholar
Pakdemirli, M. and Elmas, N., ‘Perturbation theorems for estimating magnitudes of roots of polynomials’, Appl. Math. Comput. 216 (2010) 1645–1651.Google Scholar
Pakdemirli, M. and Yurtsever, H. A., ‘Estimating roots of polynomials using perturbation theory’, Appl. Math. Comput. 188 (2007) 2025–2028.Google Scholar
Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T., Numerical recipes (Cambridge University Press, New York, 1989).Google Scholar