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

1986 ◽  
Vol 12 (4) ◽  
pp. 295-306 ◽  
Author(s):  
G. V. Milovanovic ◽  
M. S. Petkovic
Keyword(s):  
Iterative Methods ◽  
Computational Efficiency ◽  
Simultaneous Approximation ◽  
Polynomial Zeros

scholarly journals Unified Convergence Analysis of Chebyshev–Halley Methods for Multiple Polynomial Zeros

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 135
Author(s):  
Stoil I. Ivanov
Keyword(s):  
Convergence Analysis ◽  
Iterative Methods ◽  
Error Estimates ◽  
Local Convergence ◽  
Initial Conditions ◽  
Extended Version ◽  
Unified Approach ◽  
Polynomial Zeros ◽  
Convergence Results ◽  
Appl Math

In this paper, we establish two local convergence theorems that provide initial conditions and error estimates to guarantee the Q-convergence of an extended version of Chebyshev–Halley family of iterative methods for multiple polynomial zeros due to Osada (J. Comput. Appl. Math. 2008, 216, 585–599). Our results unify and complement earlier local convergence results about Halley, Chebyshev and Super–Halley methods for multiple polynomial zeros. To the best of our knowledge, the results about the Osada’s method for multiple polynomial zeros are the first of their kind in the literature. Moreover, our unified approach allows us to compare the convergence domains and error estimates of the mentioned famous methods and several new randomly generated methods.

On Euler-like methods for the simultaneous approximation of polynomial zeros

1998 ◽  
Vol 15 (2) ◽  
pp. 295-315 ◽  
Author(s):  
Miodrag S. Petković ◽  
Slobodan Tričković ◽  
Djordje Herceg
Keyword(s):  
Simultaneous Approximation ◽  
Polynomial Zeros
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