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Table 3 Implemented weight parameter and optimal weight parameter of operator S

From: An inertial parallel algorithm for a finite family of G-nonexpansive mappings with application to the diffusion problem

The different types of operator S Implement weight parameter ω Optimal weight parameter \(\omega _{o}\)
\(S^{\mathrm{WJ}} \) \(0 < \omega < 2\min \{ \frac{\lambda _{\min }(D)}{\lambda _{\min }(A)}, \frac{\lambda _{\max }(D)}{\lambda _{\max }(A)} \} \) \(\omega _{o} =\frac{1}{2} ( \lambda _{\min }(A) + \lambda _{\max }(A) )\)
\(S^{\mathrm{SOR}}\) 0<ω<2 \(\omega _{o} = \frac{2d}{d + \sqrt{\lambda _{\min }(A) \lambda _{\max }(A)}}\)