Table 1 Numerical results for Example 1
From: Strong convergence of an inertial algorithm for maximal monotone inclusions with applications
Algorithm (1.5) | Algorithm (1.7) (Inertial PPA) | Algorithm (3.1) (Inertial Algorithm 1) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
IP | n | \(\|u_{n+1}\|\) | T (s) | IP | n | \(\|u_{n+1}\|\) | T (s) | IP | n | \(\|u_{n+1}\|\) | T (s) |
\(u_{1}(t)=t^{2}+1\) | 10 | 0.3587 | 0.032 | \(u_{1}(t)=t^{2}+1\) | 10 | 0.0762 | 0.081 | \(u_{0}(t)= 2t\) \(u_{1}(t)=t^{2}+1\) | 10 | 1.999E−6 | 15.69 |
\(u_{1}(t)=\frac{1}{t+1}\) | 10 | 0.2093 | 0.058 | \(u_{1}(t)=\frac{1}{t+1}\) | 10 | 0.1056 | 0.082 | \(u_{0}(t)= 2t\) \(u_{1}(t)=\frac{1}{t+1}\) | 10 | 1.87E−6 | 17.65 |
\(u_{1}(t)=te^{t}\) | 10 | 0.2984 | 0.056 | \(u_{1}(t)=te^{t}\) | 10 | 0.0552 | 0.095 | \(u_{0}(t)= 2t\) \(u_{1}(t)=te^{t}\) | 8 | 1.89E−6 | 92.44 |