Preconditioning Complex Symmetric Linear Systems

Table 1

Numerical results for COCG, COCR, and QMR preconditioned on the basis of the complex matrix with LU decomposition, with incomplete LU (ILU) and with incomplete LU with threshold (ILU0). The reported numbers represent the iterations of the corresponding solver with the specified preconditioner. The dash indicates that it was not feasible to compute a particular test. The column “preconditioner” shows the time required to assemble the preconditioner. The stopping tolerance was . The time elapsed in the computation is expressed in seconds.

Test case	Preconditioner			COCG		COCR		QMR
	LU	ILU0	ILU	ILU0	ILU	ILU0	ILU	No Preco	ILU0	ILU
T5k
Iter.				86	9	86	9		85	8
Time	0.59	0.027	1.28	0.21	1.34	0.22	1.34	—	0.65	1.73
T16k
Iter.				65	6	65	6	399	64	5
Time	13.9	0.08	315	0.44	317	0.44	317	1.75	1.35	337
T80k
Iter.					204		205			200
Time	21.8	0.26	49.6	—	73	—	74	—	—	266
T150k
Iter.				661	24	634	24		642	23
Time	13.0	0.058	152	12.7	156	13.1	156	—	40.4	174
T500k
Iter.
Time	—	0.79	—	—	—	—	—	—	—	—
S13k
Iter.					1253		1258		2152	1307
Time	—	0.032	6.15	—	36.5	—	36.7	—	29.4	333
S32k
Iter.
Time	—	0.082	28	—	—	—	—	—	—	—
S500k
Iter.
Time	—	—	—	—	—	—	—	—	—	—