New optimal class of higher-order methods for multiple roots, permitting f′(xn)=0

2013 ◽  
Vol 222 ◽  
pp. 564-574 ◽  
Author(s):  
V. Kanwar ◽  
Saurabh Bhatia ◽  
Munish Kansal
Keyword(s):  
Higher Order ◽  
Multiple Roots ◽  
Higher Order Methods

scholarly journals Memorizing Schröder’s Method as an Efficient Strategy for Estimating Roots of Unknown Multiplicity

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2570
Author(s):  
Alicia Cordero ◽  
Beny Neta ◽  
Juan R. Torregrosa
Keyword(s):  
Order Of Convergence ◽  
Iterative Scheme ◽  
Basins Of Attraction ◽  
Higher Order ◽  
Multiple Roots ◽  
Higher Order Methods ◽  
Efficient Strategy ◽  
Schröder’S Method ◽  
With Memory

In this paper, we propose, to the best of our knowledge, the first iterative scheme with memory for finding roots whose multiplicity is unknown existing in the literature. It improves the efficiency of a similar procedure without memory due to Schröder and can be considered as a seed to generate higher order methods with similar characteristics. Once its order of convergence is studied, its stability is analyzed showing its good properties, and it is compared numerically in terms of their basins of attraction with similar schemes without memory for finding multiple roots.

scholarly journals An Optimal Fourth Order Derivative-Free Numerical Algorithm for Multiple Roots

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1038 ◽  
Author(s):  
Sunil Kumar ◽  
Deepak Kumar ◽  
Janak Raj Sharma ◽  
Clemente Cesarano ◽  
Praveen Agarwal ◽  
...  
Keyword(s):  
Iterative Methods ◽  
Numerical Algorithm ◽  
Fourth Order ◽  
Iterative Scheme ◽  
Higher Order ◽  
New Technique ◽  
Multiple Roots ◽  
Order Convergence ◽  
Higher Order Methods ◽  
Derivative Free

A plethora of higher order iterative methods, involving derivatives in algorithms, are available in the literature for finding multiple roots. Contrary to this fact, the higher order methods without derivatives in the iteration are difficult to construct, and hence, such methods are almost non-existent. This motivated us to explore a derivative-free iterative scheme with optimal fourth order convergence. The applicability of the new scheme is shown by testing on different functions, which illustrates the excellent convergence. Moreover, the comparison of the performance shows that the new technique is a good competitor to existing optimal fourth order Newton-like techniques.

A Comparison of Higher-Order Methods on a Set of Canonical Aerodynamics Applications

2011 ◽  
Author(s):  
Julie Andren ◽  
Haiyang Gao ◽  
Masayuki Yano ◽  
David Darmofal ◽  
Carl Ollivier Gooch ◽  
...  
Keyword(s):  
Higher Order ◽  
Higher Order Methods

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

2011 ◽  
Vol 58 (2) ◽  
pp. 179-201 ◽  
Author(s):  
Miodrag S. Petković ◽  
Mimica R. Milošević ◽  
Dušan M. Milošević
Keyword(s):  
Higher Order ◽  
Polynomial Zeros ◽  
Higher Order Methods
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