The self-validated method for polynomial zeros of high efficiency

Authors:
Miodrag S. Petković
Affiliations:
Faculty of Electronic Engineering, Department of Mathematics, University of Niš, 18000 Niš, Serbia
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 7
Cited 1

On computational efficiency of the iterative methods for the simultaneous approximation of polynomial zeros

ACM Transactions on Mathematical Software (TOMS)
On Halley-like algorithms for simultaneous approximation of polynomial complex zeros

SIAM Journal on Numerical Analysis
An improvement of Gargantini's simultaneous inclusion method for polynomial roots by Schro¨der's correction

Applied Numerical Mathematics
Algorithm 786: multiple-precision complex arithmetic and functions

ACM Transactions on Mathematical Software (TOMS)
Halley-like method with corrections for the inclusion of polynomial zeros

Computing
A modified Newton method for polynomials

Communications of the ACM
MPFR: A multiple-precision binary floating-point library with correct rounding

ACM Transactions on Mathematical Software (TOMS)

New higher-order methods for the simultaneous inclusion of polynomial zeros

Numerical Algorithms

Quantified Score

Hi-index	7.29

Visualization

Abstract

The improved iterative method of Newton's type for the simultaneous inclusion of all simple complex zeros of a polynomial is proposed. The presented convergence analysis, which uses the concept of the R-order of convergence of mutually dependent sequences, shows that the convergence rate of the basic third order method is increased from 3 to 6 using Ostrowski's corrections. The new inclusion method with Ostrowski's corrections is more efficient compared to all existing methods belonging to the same class. To demonstrate the convergence properties of the proposed method, two numerical examples are given.