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

Authors:
G. V. Milovanovic;M. S. Petkovic
Affiliations:
Univ. of Nisˇ, Nisˇ, Yugoslavia;Univ. of Nisˇ, Nisˇ, Yugoslavia
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
1986

Citing 2
Cited 5

Iterative solution of nonlinear equations in several variables

Iterative solution of nonlinear equations in several variables
A modified Newton method for polynomials

Communications of the ACM

The mathematical basis and a prototype implementation of a new polynomial rootfinder with quadratic convergence

ACM Transactions on Mathematical Software (TOMS)
A neural root finder of polynomials based on root moments

Neural Computation
The self-validated method for polynomial zeros of high efficiency

Journal of Computational and Applied Mathematics
Accelerating generators of iterative methods for finding multiple roots of nonlinear equations

Computers & Mathematics with Applications
Efficient polynomial root-refiners: A survey and new record efficiency estimates

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

A measure of efficiency of simultaneous methods for determination of polynomial zeros, defined by the coefficient of efficiency, is considered. This coefficient takes into consideration (1) the R-order of convergence in the sense of the definition introduced by Ortega and Rheinboldt (Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York, 1970) and (2) the number of basic arithmetic operations per iteration, taken with certain weights depending on a processor time. The introduced definition of computational efficiency was used for comparison of the simultaneous methods with various structures.