Theory and Modern Applications
Method | n | CPU | ρ | \(\Vert \mathbf{x}^{(k+1)}-\mathbf{x}^{(k)} \Vert \) | \(\Vert \mathbf{Fx}^{(k)} \Vert \) |
---|---|---|---|---|---|
Solving a system of nonlinear equations \(\mathbf{F}_{3}(\mathbf{X}) \) and \(\mathbf{F}_{4}(\mathbf{X})\) | |||||
\(\mathbf{F}_{3}(\mathbf{X})\); \((\mathbf{1.5},\mathbf{1.5})^{T}\); \(\mathbf{X}_{0}=(\mathbf{0.8},\mathbf{1},\mathbf{0.8})^{T}\), \(\alpha =\frac{-1}{100{,}000}\) | |||||
QQ1 | 3 | 0.015 | 3.3 | 1.7e−31 | 5.1e−32 |
EE1 | 3 | 0.016 | 3.0 | 1.2e−17 | 1.1e−17 |
EE2 | 3 | 0.017 | 2.9 | 2.3e−16 | 2.1e−17 |
EE3 | 3 | 0.017 | 3.0 | 2.5e−17 | 2.1e−17 |
\(\mathbf{F}_{4}(\mathbf{X})\); \(\mathbf{X}_{0}=(\mathbf{0.5},\mathbf{0.5},\mathbf{0.5})^{T}\), \(\alpha =\frac{-1}{100{,}000}\) | |||||
QQ1 | 3 | 0.013 | 3.0 | 9.9e−11 | 1.7e−21 |
EE1 | 3 | 0.031 | 2.7 | 1.1e−7 | 4.0e−18 |
EE2 | 3 | 0.016 | 3.0 | 2.3e−16 | 8.1e−18 |
EE3 | 3 | 0.016 | 2.9 | 9.0e−11 | 2.3e−17 |