Table 2 Numerical results for Example 5.2 ( \(\pmb{\rho=\rho_{n}=0.001}\) )
From: New strong convergence theorems for split variational inclusion problems in Hilbert spaces
\(\boldsymbol{x_{1}=(1,1)^{\top}}\) | \(\boldsymbol{\varepsilon=10^{-3}}\) | \(\boldsymbol{\varepsilon=10^{-4}}\) | ||||
|---|---|---|---|---|---|---|
Time | Iteration | Approximate solution | Time | Iteration | Approximate solution | |
Algorithm 1.2 | ≤ | 20 | (0.4872068,−0.5128408) | 0.02 | 61 | (0.4953678 − 0.5046371) |
Theorem 1.1 | 0.02 | 157 | (1.382916,0.3832697) | 0.26 | 3,035 | (0.5882673,−0.4116973328) |
\(\boldsymbol{x_{1}=(1,1)^{\top}}\) | \(\boldsymbol{\varepsilon=10^{-5}}\) | \(\boldsymbol{\varepsilon=10^{-6}}\) | ||||
|---|---|---|---|---|---|---|
Time | Iteration | Approximate solution | Time | Iteration | Approximate solution | |
Algorithm 1.2 | 0.07 | 209 | (0.4985109,−0.5014895) | 0.19 | 716 | (0.4996333,−0.5003667) |
Theorem 1.1 | 0.56 | 5,912 | (0.5088314,−0.4911650960) | 0.90 | 8,790 | (0.5008829,−0.4991167527) |
\(\boldsymbol{x_{1}=(1,1)^{\top}}\) | \(\boldsymbol{\varepsilon=10^{-7}}\) | \(\boldsymbol{\varepsilon=10^{-8}}\) | ||||
|---|---|---|---|---|---|---|
Time | Iteration | Approximate solution | Time | Iteration | Approximate solution | |
Algorithm 1.2 | 0.49 | 1,984 | (0.4999414,−0.5000586) | 1.04 | 3,944 | (0.4999930,−0.5000070) |
Theorem 1.1 | 1.33 | 11,668 | (0.5000883,−0.4999116996) | 1.79 | 14,545 | (0.5000088,−0.4999911653) |