Table 8 Numerical results of Example 4.6 for the initial points \(x_{0} = (-1,2,1)^{T}\) and \(x_{1} = (2,-1,-2)^{T}\) using Algorithm 3 in Theorem 4.1
Type | \(\lambda _{n}\) for \(L_{1}=1\) | n | CPU (s) | \(x^{*}\) | \(\|x_{n+1}-x_{n}\|_{2}\) |
|---|---|---|---|---|---|
A1 | \(\frac{L_{1}}{10}\) | 142 | 0.546 | \((1.00001,2.00000,2.99999)^{T}\) | 8.78 × 10−7 |
A2 | \(L_{1}-\frac{L_{1}}{10}\) | 49 | 0.046 | \((1.00001,2.00001,3.00001)^{T}\) | 9.60 × 10−7 |
A3 | \(L_{1}\) | 48 | 0.047 | \((1.00001,2.00001,3.00001)^{T}\) | 9.38 × 10−7 |
A4 | \(L_{1}+\frac{L_{1}}{10}\) | 47 | 0.063 | \((1.00001,2.00001,3.00001)^{T}\) | 9.27 × 10−7 |
A5 | \(2L_{1}-\frac{L_{1}}{10}\) | – | – | – | – |
A6 | \(2L_{1}\) | – | – | – | – |
B1 | \(\frac{L_{1} n}{n+1}\) | 48 | 0.046 | \((1.00001,2.00001,3.00001)^{T}\) | 9.65 × 10−7 |
B2 | \(\frac{L_{1} (n+2)}{n+1}\) | 47 | 0.046 | \((1.00001,2.00001,3.00001)^{T}\) | 9.92 × 10−7 |
B3 | \(\frac{2 L_{1} n}{n+1}\) | – | – | – | – |
C1 | \(L_{1}+\frac{(-1)^{n} L_{1}}{n+1}\) | 37 | 0.031 | \((1.00002,2.00002,3.00002)^{T}\) | 8.75 × 10−7 |
C2 | \(L_{1}+\frac{(-1)^{n+1}L_{1}}{n+1}\) | 36 | 0.031 | \((1.00002,2.00002,3.00002)^{T}\) | 9.74 × 10−7 |