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Table 4 Comparison of optimal 3rd order methods

From: On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation

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