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