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

Table 1

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

	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	0.8	0.8	0.8	0.8
	𝜌(𝑀𝛼^∗𝑃)	0.6638	0.6672	0.6684	0.6690
GPMHSS	𝛼^∗𝐺	0.8	0.8	0.8	0.8
	𝛽^∗𝐺	3	2	1.6	1.4
	𝜌(𝑀𝛼^∗𝐺,𝛽^∗𝐺)	0.4618	0.4851	0.5096	0.5321