Circular arithmetic and the determination of polynomial zeros

1971 ◽  
Vol 18 (4) ◽  
pp. 305-320 ◽  
Author(s):  
Irene Gargantini ◽  
Peter Henrici
Keyword(s):  
Polynomial Zeros ◽  
Circular Arithmetic

scholarly journals Derivative free method for the simultaneous inclusion of polynomial zeros

Filomat ◽  
2003 ◽  
pp. 155-168
Author(s):  
Miodrag Petkovic ◽  
Dusan Milosevic
Keyword(s):  
Order Of Convergence ◽  
Initial Conditions ◽  
Convergence Speed ◽  
Combined Method ◽  
Polynomial Zeros ◽  
Numerical Example ◽  
Derivative Free ◽  
Circular Arithmetic ◽  
Derivative Free Method ◽  
Complex Zeros

A combined method for the simultaneous inclusion of complex zeros of a polynomial, composed of two circular arithmetic methods, is presented. This method does not use polynomial derivatives and has the order of convergence equals four. Computationally variable initial conditions that guarantee the convergence are also stated. Two numerical example are included to demonstrate the convergence speed of the presented method.

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
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