Weak convergence theorems for split feasibility problems on zeros of the sum of monotone operators and fixed point sets in Hilbert spaces

Suwannaprapa, Montira; Petrot, Narin; Suantai, Suthep

doi:10.1186/s13663-017-0599-7

Fixed Point Theory and Algorithms for Sciences and Engineering

Table 3 Influence of the step size parameters \(\pmb{\lambda_{n}}\) and \(\pmb{\gamma_{n}}\) for the initial vector \(\pmb{(1,-1)}\) with the 4 decimal places

From: Weak convergence theorems for split feasibility problems on zeros of the sum of monotone operators and fixed point sets in Hilbert spaces

Case →	1		2		3		4		5
#(Iters) ↓	\(\boldsymbol{x_{\mathrm{Iter}}}\)	Errors	\(\boldsymbol{x_{\mathrm{Iter}}}\)	Errors	\(\boldsymbol{x_{\mathrm{Iter}}}\)	Errors	\(\boldsymbol{x_{\mathrm{Iter}}}\)	Errors	\(\boldsymbol{x_{\mathrm{Iter}}}\)	Errors
50	\(\begin{pmatrix} 0.6997\\0.1331 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.8477\\0.0097 \end{pmatrix} \)	0.1848	\(\begin{pmatrix} 0.8477\\0.0097 \end{pmatrix} \)	0.1848	\(\begin{pmatrix} 0.6758\\0.1172 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.6758\\0.1172 \end{pmatrix} \)	0
60	\(\begin{pmatrix} 0.6997\\0.1331 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.8457\\0.0126 \end{pmatrix} \)	0.1813	\(\begin{pmatrix} 0.8457\\0.0126 \end{pmatrix} \)	0.1813	\(\begin{pmatrix} 0.6758\\0.1172 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.6758\\0.1172 \end{pmatrix} \)	0
120	\(\begin{pmatrix} 0.6997\\0.1331 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.8384\\0.0236 \end{pmatrix} \)	0.1681	\(\begin{pmatrix} 0.8384\\0.0236 \end{pmatrix} \)	0.1681	\(\begin{pmatrix} 0.6758\\0.1172 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.6758\\0.1172 \end{pmatrix} \)	0
50,000	\(\begin{pmatrix} 0.6997\\0.1331 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.7455\\0.1629 \end{pmatrix} \)	\(6.3791e^{-04}\)	\(\begin{pmatrix} 0.7455\\0.1629 \end{pmatrix} \)	\(6.3791e^{-04}\)	\(\begin{pmatrix} 0.6758\\0.1172 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.6758\\0.1172 \end{pmatrix} \)	0
75,000	\(\begin{pmatrix} 0.6997\\0.1331 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.7452\\0.1634 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.7452\\0.1634 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.6758\\0.1172 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.6758\\0.1172 \end{pmatrix} \)	0

Back to article page