Deflated preconditioned conjugate gradient method for solving single-step BLUP models efficiently

Table 3 Characteristics of preconditioned (deflated) coefficient matrices, and of PCG and DPCG methods for the reduced dataset

Model	Method^a	Smallest eigenvalue	Largest eigenvalue	Effective condition number	Number of iterations	Total time^b	Time/iteration^c
ssGBLUP	PCG	1.1 × 10⁻⁴	11.9	1.1 × 10⁵	270	11.3	0.05
ssSNPBLUP	PCG	1.1 × 10⁻⁴	181.0	1.7 × 10⁶	1475	688.2	0.46
	DPCG (200)	1.1 × 10⁻⁴	99.4	9.3 × 10⁵	1221	570.5	0.47
	DPCG (50)	1.1 × 10⁻⁴	40.5	3.8 × 10⁵	890	437.7	0.49
	DPCG (5)	1.1 × 10⁻⁴	6.4	6.0 × 10⁴	331	170.1	0.49
	DPCG (1)	1.1 × 10⁻⁴	6.0	5.9 × 10⁴	270	189.6	0.66

^aNumber of SNP effects per subdomain is within brackets
^bWall clock time (s) for the iterative process
^cAverage wall clock time (s) per iteration. Iterations computing the residual from the coefficient matrix for the PCG method were removed before averaging

ISSN: 1297-9686