Skip to main content

Table 1 The best choice types of testing the parameters \(\gamma _{n}\), \(\lambda _{n}\), and \(\eta _{n}\) for the fast convergence

From: Split monotone variational inclusion with errors for image-feature extraction with multiple-image blends problem

Type

\(\gamma _{n}\)

\(\lambda _{n}\)

\(\eta _{n}\)

A1

\(\frac{L_{0}}{10}\)

\(\frac{L_{1}}{10}\)

\(\frac{L_{2}}{10}\)

A2

\(L_{0}-\frac{L_{0}}{10}\)

\(L_{1}-\frac{L_{1}}{10}\)

\(L_{2}-\frac{L_{2}}{10}\)

A3

\(L_{0}\)

\(L_{1}\)

\(L_{2}\)

A4

\(L_{0}+\frac{L_{0}}{10}\)

\(L_{1}+\frac{L_{1}}{10}\)

\(L_{2}+\frac{L_{2}}{10}\)

A5

\(2L_{0}-\frac{L_{0}}{10}\)

\(2L_{1}-\frac{L_{1}}{10}\)

\(2L_{2}-\frac{L_{2}}{10}\)

A6

\(2L_{1}\)

\(2L_{2}\)

B1

\(\frac{L_{0} n}{n+1}\)

\(\frac{L_{1} n}{n+1}\)

\(\frac{L_{2} n}{n+1}\)

B2

\(\frac{L_{0} (n+2)}{n+1}\)

\(\frac{L_{1} (n+2)}{n+1}\)

\(\frac{L_{2} (n+2)}{n+1}\)

B3

\(\frac{2L_{1} n}{n+1}\)

\(\frac{2L_{2} n}{n+1}\)

C1

\(L_{0}+\frac{(-1)^{n} L_{0}}{n+1}\)

\(L_{1}+\frac{(-1)^{n} L_{1}}{n+1}\)

\(L_{2}+\frac{(-1)^{n} L_{2}}{n+1}\)

C2

\(L_{0}+\frac{(-1)^{n+1} L_{0}}{n+1}\)

\(L_{1}+\frac{(-1)^{n+1} L_{1}}{n+1}\)

\(L_{2}+\frac{(-1)^{n+1} L_{2}}{n+1}\)