IJPAM: Volume 46, No. 2 (2008)

Invited Lecture Delivered at
Forth International Conference of Applied Mathematics
and Computing (Plovdiv, Bulgaria, August 12-18, 2007)


D.M. Miloševic$^1$, Lj.D. Petkovic$^2$, M.S. Petkovic$^3$
$^{1,3}$Faculty of Electronic Engineering
University of Niš
Niš, 18000, SERBIA
$^1$e-mail: dmilosev@elfak.ni.ac.yu
$^2$Faculty of Mechanical Engineering
University of Niš
Niš, 18000, SERBIA

Abstract.The computed roots of algebraic equations are only approximations to the exact roots since there are errors originating from discretization, truncation and from rounding. For this reason, it is important to apply a root-finding procedure which simultaneously improves the approximations to the roots and also gives error bounds of the improved approximations. In this paper we study three types of self-validated methods that automatically provide upper error bounds of the computed approximations: (I) interval methods which deal with disks as arguments, (II) hybrid methods that combine a simultaneous method in ordinary complex arithmetic and an interval method in circular complex interval arithmetic, and (III) a posteriori bound error methods. Numerical examples illustrate each of the presented approaches.

Received: August 17, 2007

AMS Subject Classification: 65H05, 65G20, 30C15

Key Words and Phrases: polynomial zeros, simultaneous methods, approximate zeros, interval methods, error bounds

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 46
Issue: 2