Convergent Homotopy Analysis Method for Solving Linear Systems

Table 4

The basic method is divergent (Theorem 3).

Matrix	Method	𝜌(𝐺)	Convergence interval	ℏopt	𝜌(𝐺ℏopt)
Si2	SOR (𝑟=𝑤=1.3)	1.0993	(0, 0.8415)	0.8	0.9974
Si2	AOR (𝑟=1.5, 𝑤=0.75)	1.0799	(0, 2.7964)	2.7	0.9942
Si2	SSOR (𝑟=𝑤=1.8)	1.24945	(0, 2.0007)	1.9	0.9909
Si2	SAOR (𝑟=1.5, 𝑤=0.75)	1.1380	(0, 2.0949)	2	0.9916
Si2	Jacobi	1.3233	(0, 0.3705)	0.7	0.9999
Si2	Richardson	40.3813	(0, 0.0012)	0.0011	0.9999