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Table 1 Numerical results for Example  5.1 ( \(\pmb{\rho=\rho_{n}=0.01}\) )

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

0.02

19

(0.9853714,−0.01460836)

0.02

60

(0.9932032,−0.006789955)

Theorem 1.1

0.01

218

(1.087499,0.08749895)

0.05

505

(1.008727,0.008726755)

Theorem 1.2

0.04

213

(1.237467,0.2433358)

0.08

939

(1.065859,0.06719048)

Theorem 1.3

0.01

137

(1.376151,0.3943719)

0.14

1,308

(1.094086,0.09599743)

Theorem 1.4

0.02

206

(1.083916,0.08392859)

0.06

484

(1.007433,0.007437749)

\(\boldsymbol{x_{1}=(1,1)^{\top}}\)

\(\boldsymbol{\varepsilon=10^{-5}}\)

\(\boldsymbol{\varepsilon=10^{-6}}\)

Time

Iteration

Approximate solution

Time

Iteration

Approximate solution

Algorithm 1.2

0.06

287

(0.9977524,−0.002246182)

0.25

970

(0.9993371,−0.0006624296)

Theorem 1.1

0.06

792

(1.000870,0.0008703675)

0.08

1,078

(1.000088,8.750662e − 05)

Theorem 1.2

0.25

2,974

(1.020805,0.02122562)

0.99

9,403

(1.006580,0.006713283)

Theorem 1.3

0.34

4,205

(1.029428,0.03002226)

1.59

13,297

(1.009306,0.009494477)

Theorem 1.4

0.07

749

(1.000037,4.018706e − 05)

0.07

953

(0.9994309,−5.664470e − 04)

\(\boldsymbol{x_{1}=(1,1)^{\top}}\)

\(\boldsymbol{\varepsilon=10^{-7}}\)

\(\boldsymbol{\varepsilon=10^{-8}}\)

Time

Iteration

Approximate solution

Time

Iteration

Approximate solution

Algorithm 1.2

0.75

2,999

(0.9997898,−0.0002100474)

2.62

9,426

(0.9999335,−6.645199e − 05)

Theorem 1.1

0.11

1,365

(1.000009,8.727519e − 06)

0.14

1,562

(1.000001,8.704438e − 07)

Theorem 1.2

5.03

29,732

(1.002081,0.002123133)

19.63

94,018

(1.000658,0.000671414)

Theorem 1.3

8.73

42,047

(1.002943,0.003002578)

21.03

132,961

(1.000931,0.0009495180)

Theorem 1.4

0.09

1,034

(0.9994033,−5.942738e − 04)

0.09

1,047

(0.9994030,−5.945951e − 04)