Generalized Preconditioned MHSS Method for a Class of Complex Symmetric Linear Systems

Table 2

The experimentally optimal parameters and the spectral radii for the iteration matrices of MHSS, PMHSS, and GPMHSS with 𝑃=𝑃₁=𝑃₂=𝑇.

	𝑚	8×8	16×16	24×24	32×32
MHSS	𝛼^∗𝑀	3.7	2.1	1.5	1.2
	𝜌(𝑀𝛼^∗𝑀)	0.7203	0.7989	0.8407	0.8662
PMHSS	𝛼^∗𝑃	1.2	1.2	1.2	1.2
	𝜌(𝑀𝛼^∗𝑃)	0.6636	0.6671	0.6684	0.6690
GPMHSS	𝛼^∗𝐺	1.2	1.2	1.2	1.2
	𝛽^∗𝐺	6.4	2.2	1.9	1.8
	𝜌(𝑀𝛼^∗𝐺,𝛽^∗𝐺)	0.3389	0.4814	0.5184	0.5461