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Table 3 Numerical results for Example 2

From: Strong convergence of an inertial algorithm for maximal monotone inclusions with applications

Algorithm (4.8)

Algorithm (4.9)

Algorithm (4.7) (Inertial Algorithm 2)

IP

n

\(\|u_{n+1}\|\)

T (s)

IP

n

\(\|u_{n+1}\|\)

T (s)

IP

n

\(\|u_{n+1}\|\)

T (s)

\(u_{1}(t)=\sin t\)

\(v_{1}(t)=\cos t\)

6

0.5193

41.56

\(u_{1}(t)=\sin t\)

\(v_{1}(t)=\cos t\)

6

0.0337

92.78

\(u_{1}(t)=\sin t\)

\(v_{1}(t)=\cos t\)

6

0.0291

4129.97

\(u_{1}(t)=t^{2}-2\)

\(v_{1}=e^{t}-1\)

6

1.2381

244.31

\(u_{1}=t^{2}-2\)

\(v_{1}=e^{t}-1\)

6

0.0463

28.55

\(u_{1}=t^{2}-2\)

\(v_{1}=e^{t}-1\)

6

0.0424

884.05

\(u_{1}(t)= 2t^{3}-2 \)

\(v_{1}=te^{t}+2t\)

6

1.4154

647.69

\(u_{1}=2t^{3}-2 \)

\(v_{1}=te^{t}+2t\)

6

0.0720

57.03

\(u_{1}=2t^{3}-2 \)

\(v_{1}=te^{t}+2t\)

6

0.0519

2268.58