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 1 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	\(\begin{pmatrix} 0.4924\\0 \end{pmatrix} \)	0.0076	\(\begin{pmatrix} 0.0343\\0.5622 \end{pmatrix} \)	0.7300	\(\begin{pmatrix} 0.0343\\0.5622 \end{pmatrix} \)	0.7300	\(\begin{pmatrix} 0.4999\\0 \end{pmatrix} \)	\(1.0e^{-04}\)	\(\begin{pmatrix} 0.4999\\0 \end{pmatrix} \)	\(1.0e^{-04}\)
60	\(\begin{pmatrix} 0.4966\\0 \end{pmatrix} \)	0.0034	\(\begin{pmatrix} 0.0420\\0.5505 \end{pmatrix} \)	0.7161	\(\begin{pmatrix} 0.0420\\0.5505 \end{pmatrix} \)	0.7161	\(\begin{pmatrix} 0.5000\\0 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.5000\\0 \end{pmatrix} \)	0
120	\(\begin{pmatrix} 0.5000\\0 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.0708\\0.5073 \end{pmatrix} \)	0.6645	\(\begin{pmatrix} 0.0708\\0.5073 \end{pmatrix} \)	0.6645	\(\begin{pmatrix} 0.5000\\0 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.5000\\0 \end{pmatrix} \)	0
250,000	\(\begin{pmatrix} 0.5000\\0 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.4999\\0 \end{pmatrix} \)	\(1.0e^{-04}\)	\(\begin{pmatrix} 0.4999\\0 \end{pmatrix} \)	\(1.0e^{-04}\)	\(\begin{pmatrix} 0.5000\\0 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.5000\\0 \end{pmatrix} \)	0
275,000	\(\begin{pmatrix} 0.5000\\0 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.5000\\0 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.5000\\0 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.5000\\0 \end{pmatrix} \)	0	\(\begin{pmatrix} 0.5000\\0 \end{pmatrix} \)	0

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