IJPAM: Volume 64, No. 3 (2010)

ON THE CRITICAL POINTS OF MAEHLY-ABERTH-EHRLICH
METHOD. GLOBAL CONVERGENCE PROPERTIES

Nikola Valchanov$^1$, Anton Iliev$^2$, Nikolay Kyurkchiev$^3$
$^{1,2,3}$Faculty of Mathematics and Informatics
University of Plovdiv ``Paisii Hilendarski''
24, Tsar Assen Str., Plovdiv, 4000, BULGARIA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]
$^3$e-mail: [email protected]


Abstract.This paper gives sufficient conditions for $k$-th approximations of the zeros of polynomial $f(x)$ when the Maehly-Aberth-Ehrlich method fails on the next step. All non-attractive sets are found for the users of this type of methods and this is a further improvement of previously developed methods and known results. Numerical and graphical examples are presented.

Received: September 18, 2010

AMS Subject Classification: 65H05

Key Words and Phrases: polynomial roots, critical initial approximations, Maehly-Aberth-Ehrlich method, divergent sets

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 3