Parallel Rayleigh Quotient Optimization with FSAI-Based Preconditioning

Table 2

Number of iterations, timings, and scalability indices for FSAI-DACG in the computation of the 10 leftmost eigenpairs of the four test problems.

	𝑝	iter	𝑇prec	𝑇iter	𝑇tot	𝑆^𝑝(4)	𝐸^𝑝(4)
FAULT-639	4	4448	25.9	261.4	287.3
	8	4448	13.2	139.0	152.2	7.6	0.94
	16	4448	6.6	69.4	76.0	15.1	0.95
	32	4448	4.0	28.2	32.2	35.7	1.11
	64	4448	1.9	15.5	17.4	66.1	1.03
	128	4448	1.1	9.4	10.5	109.0	0.85
PO-878	4	5876	48.1	722.5	770.6
	8	5876	25.2	399.8	425.0	7.3	0.91
	16	5876	11.4	130.2	141.6	21.8	1.36
	32	5876	6.8	65.8	72.5	42.5	1.33
	64	5876	4.1	30.1	34.1	90.3	1.41
	128	5876	1.9	19.1	21.0	146.8	1.15
GEO-1437	4	6216	90.3	901.5	991.7
	8	6216	47.5	478.9	526.4	7.5	0.94
	16	6216	24.7	239.4	264.1	15.0	0.94
	32	6216	13.6	121.0	134.6	29.5	0.92
	64	6216	8.2	60.9	69.1	57.4	0.90
	128	6216	4.2	29.5	33.8	117.5	0.92
	256	6216	2.3	19.1	21.4	185.4	0.72
	𝑝	iter	𝑇prec	𝑇iter	𝑇tot	𝑆^𝑝(16)	𝐸^𝑝(16)
CUBE-6091	16	15796	121.5	2624.8	2746.2
	32	15796	62.2	1343.8	1406.0	31.3	0.98
	64	15796	32.5	737.0	769.5	57.1	0.89
	128	15796	17.3	388.4	405.7	108.3	0.85
	256	15796	9.1	183.9	192.9	227.8	0.89
	512	15796	5.7	106.0	111.7	393.5	0.77
	1024	15796	3.8	76.6	80.4	546.6	0.53