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# Table 4 Comparison of optimal 3rd order methods

Method |
n
| CPU |
ρ
| \(\Vert \mathbf{x}^{(k+1)}-\mathbf{x}^{(k)} \Vert \) | \(\Vert \mathbf{Fx}^{(k)} \Vert \) |
---|---|---|---|---|---|

Solving a system of nonlinear equations \(\mathbf{F}_{1}(\mathbf{X}) \) and \(\mathbf{F}_{2}(\mathbf{X})\) | |||||

\(\mathbf{F}_{1}(\mathbf{X})\); \((\mathbf{1.5},\mathbf{1.5})^{T}\); \(\mathbf{X}_{0}=(\mathbf{0.6},\mathbf{1.4})^{T}\), \(\alpha =\frac{-1}{100{,}000}\) | |||||

QQ1 | 3 | 0.012 | 3.0 | 7.9e−17 | 9.7e−17 |

EE1 | 3 | 0.031 | 2.9 | 3.8e−9 | 1.4e−9 |

EE2 | 3 | 0.015 | 3.0 | 5.9e−17 | 2.3e−16 |

EE3 | 3 | 0.562 | 3.0 | 2.1e−15 | 2.1e−15 |

\(\mathbf{F}_{2}(\mathbf{X})\); \(\mathbf{X}_{0}=(\mathbf{1.5},\mathbf{1.0})^{T}\), \(\alpha =\frac{-1}{100{,}000}\) | |||||

QQ1 | 4 | 0.017 | 3.1 | 1.2e−21 | 0.1e−21 |

EE1 | 4 | 0.016 | 2.9 | 8.3e−17 | 1.1e−18 |

EE2 | 4 | 0.016 | 3.0 | 1.8e−16 | 1.0e−17 |

EE3 | 4 | 0.016 | 3.0 | 5.3e−17 | 5.3e−17 |