Convergence of Newton, Halley and Chebyshev iterative methods as methods for simultaneous determination of multiple polynomial zeros

2017 ◽  
Vol 112 ◽  
pp. 146-154 ◽  
Author(s):  
Veselina K. Kyncheva ◽  
Viktor V. Yotov ◽  
Stoil I. Ivanov
Keyword(s):  
Simultaneous Determination ◽  
Iterative Methods ◽  
Polynomial Zeros

scholarly journals On Efficient Iterative Numerical Methods for Simultaneous Determination of all Roots of Non-Linear Function

2020 ◽  
Author(s):  
Mudassir Shams ◽  
Nazir Mir ◽  
Naila Rafiq
Keyword(s):  
Simultaneous Determination ◽  
Iterative Methods ◽  
Linear Equations ◽  
Basin Of Attraction ◽  
Numerical Test ◽  
Computational Cost ◽  
Single Root ◽  
Non Linear ◽  
Non Linear Equations

We construct a family of two-step optimal fourth order iterative methods for finding single root of non-linear equations. We generalize these methods to simultaneous iterative methods for determining all the distinct as well as multiple roots of single variable non-linear equations. Convergence analysis is present for both cases to show that the order of convergence is four in case of single root finding method and is twelve for simultaneous determination of all roots of non-linear equation. The computational cost, Basin of attraction, efficiency, log of residual and numerical test examples shows, the newly constructed methods are more efficient as compared to the existing methods in literature.

scholarly journals Convergence Analysis of a Modified Weierstrass Method for the Simultaneous Determination of Polynomial Zeros

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1408
Author(s):  
Plamena I. Marcheva ◽  
Stoil I. Ivanov
Keyword(s):  
Error Estimate ◽  
Convergence Analysis ◽  
Simultaneous Determination ◽  
Numerical Experiments ◽  
Practical Importance ◽  
Semilocal Convergence ◽  
Numerical Comparison ◽  
Initial Condition ◽  
Polynomial Zeros

In 2016, Nedzhibov constructed a modification of the Weierstrass method for simultaneous computation of polynomial zeros. In this work, we obtain local and semilocal convergence theorems that improve and complement the previous results about this method. The semilocal result is of significant practical importance because of its computationally verifiable initial condition and error estimate. Numerical experiments to show the applicability of our semilocal theorem are also presented. We finish this study with a theoretical and numerical comparison between the modified Weierstrass method and the classical Weierstrass method.

On some methods for the simultaneous determination of polynomial zeros

1996 ◽  
Vol 13 (2) ◽  
pp. 267-288 ◽  
Author(s):  
Sachio Kanno ◽  
Nikolai V. Kjurkchiev ◽  
Tetsuro Yamamoto
Keyword(s):  
Simultaneous Determination ◽  
Polynomial Zeros

A general computer program for the extended plate overlap algorithm

1978 ◽  
Vol 48 ◽  
pp. 287-293 ◽  
Author(s):  
Chr. de Vegt ◽  
E. Ebner ◽  
K. von der Heide
Keyword(s):  
Computer Program ◽  
Simultaneous Determination ◽  
General Computer Program ◽  
General Computer

In contrast to the adjustment of single plates a block adjustment is a simultaneous determination of all unknowns associated with many overlapping plates (star positions and plate constants etc. ) by one large adjustment. This plate overlap technique was introduced by Eichhorn and reviewed by Googe et. al. The author now has developed a set of computer programmes which allows the adjustment of any set of contemporaneous overlapping plates. There is in principle no limit for the number of plates, the number of stars, the number of individual plate constants for each plate, and for the overlapping factor.

Sign in / Sign up

Export Citation Format

Share Document