An Optimal Fourth Order Derivative-Free Numerical Algorithm for Multiple Roots
Abstract
:1. Introduction
2. Development of the Scheme
3. Generalization of the Method
4. Basins of Attraction
5. Numerical Results
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Methods | k | ACOC | CPU | |||
---|---|---|---|---|---|---|
LM−1 | 6 | 4.000 | 0.0776 | |||
LM−2 | 6 | 4.000 | 0.0942 | |||
SSM | 6 | 4.000 | 0.0782 | |||
ZM | 6 | 4.000 | 0.0634 | |||
SM | 6 | 4.000 | 0.0935 | |||
KM | 6 | 4.000 | 0.0624 | |||
SM−1 | 6 | 4.000 | 0.0724 | |||
SM−2 | 6 | 4.000 | 0.0745 | |||
NM | 5 | 4.000 | 0.0615 |
Methods | k | ACOC | CPU | |||
---|---|---|---|---|---|---|
LM−1 | 4 | 4.000 | 0.8274 | |||
LM−2 | 4 | 4.000 | 1.1072 | |||
SSM | 4 | 4.000 | 1.1076 | |||
ZM | 4 | 4.000 | 1.1066 | |||
SM | 4 | 4.000 | 1.2947 | |||
KM | 4 | 4.000 | 1.0952 | |||
SM−1 | 3 | 0 | 4.000 | 0.3284 | ||
SM−2 | 3 | 0 | 4.000 | 0.3375 | ||
NM | 3 | 0 | 4.000 | 0.3124 |
Methods | k | ACOC | CPU | |||
---|---|---|---|---|---|---|
LM−1 | 4 | 4.000 | 1.6382 | |||
LM−2 | 4 | 4.000 | 1.7935 | |||
SSM | 4 | 4.000 | 1.9031 | |||
ZM | 4 | 4.000 | 1.8720 | |||
SM | 4 | 4.000 | 1.9655 | |||
KM | 4 | 4.000 | 1.9026 | |||
SM−1 | 4 | 4.000 | 1.4802 | |||
SM−2 | 4 | 4.000 | 1.4922 | |||
NM | 4 | 4.000 | 1.4656 |
Methods | k | ACOC | CPU | |||
---|---|---|---|---|---|---|
LM−1 | 4 | 4.000 | 1.4512 | |||
LM−2 | 4 | 4.000 | 2.2314 | |||
SSM | 4 | 4.000 | 2.2615 | |||
ZM | 4 | 4.000 | 2.3088 | |||
SM | 4 | 4.000 | 2.7610 | |||
KM | 4 | 4.000 | 2.2926 | |||
SM−1 | 4 | 4.000 | 0.7223 | |||
SM−2 | 4 | 4.000 | 0.7407 | |||
NM | 4 | 4.000 | 0.5931 |
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Kumar, S.; Kumar, D.; Sharma, J.R.; Cesarano, C.; Agarwal, P.; Chu, Y.-M. An Optimal Fourth Order Derivative-Free Numerical Algorithm for Multiple Roots. Symmetry 2020, 12, 1038. https://doi.org/10.3390/sym12061038
Kumar S, Kumar D, Sharma JR, Cesarano C, Agarwal P, Chu Y-M. An Optimal Fourth Order Derivative-Free Numerical Algorithm for Multiple Roots. Symmetry. 2020; 12(6):1038. https://doi.org/10.3390/sym12061038
Chicago/Turabian StyleKumar, Sunil, Deepak Kumar, Janak Raj Sharma, Clemente Cesarano, Praveen Agarwal, and Yu-Ming Chu. 2020. "An Optimal Fourth Order Derivative-Free Numerical Algorithm for Multiple Roots" Symmetry 12, no. 6: 1038. https://doi.org/10.3390/sym12061038
APA StyleKumar, S., Kumar, D., Sharma, J. R., Cesarano, C., Agarwal, P., & Chu, Y. -M. (2020). An Optimal Fourth Order Derivative-Free Numerical Algorithm for Multiple Roots. Symmetry, 12(6), 1038. https://doi.org/10.3390/sym12061038