Table 1.

Characteristics of preconditioned (deflated) coefficient matrices, and of PCG and DPCG methods for solving ssSNPBLUP applied to the reduced dataset

${\text{Model}}^{\mathrm{a}}$	${\text{Method}}^{\mathrm{b}}$	$k_O^{\mathrm{c}}$	$k_S^{\mathrm{c}}$	$k_O/k_S$	${\lambda }_{\mathit{min}}^{\mathrm{d}}$	${\lambda }_{\mathit{max}}^{\mathrm{d}}$	${\kappa }^{\mathrm{e}}$	${\mathit{N}}^{\mathrm{f}}$
MS	PCG	1	1	1	$1.07\times {10}^{-04}$	$1.81\times {10}^2$	$1.70\times {10}^6$	1499
MS	PCG	1	2	0.5	$1.07\times {10}^{-04}$	$9.11\times {10}^1$	$8.55\times {10}^5$	1103
MS	PCG	1	3.3	0.3	$1.07\times {10}^{-04}$	$5.51\times {10}^1$	$5.17\times {10}^5$	862
MS	PCG	1	${10}^1$	${10}^{-1}$	$1.07\times {10}^{-04}$	$1.91\times {10}^1$	$1.79\times {10}^5$	560
MS	PCG	1	${10}^2$	${10}^{-2}$	$1.07\times {10}^{-04}$	$1.19\times {10}^1$	$1.12\times {10}^5$	417
MS	PCG	1	${10}^3$	${10}^{-3}$	$1.06\times {10}^{-04}$	$1.19\times {10}^1$	$1.12\times {10}^5$	608
MS	PCG	1	${10}^4$	${10}^{-4}$	$4.86\times {10}^{-05}$	$1.19\times {10}^1$	$2.45\times {10}^5$	1254
MS	PCG	1	${10}^5$	${10}^{-5}$	$4.87\times {10}^{-06}$	$1.19\times {10}^1$	$2.45\times {10}^6$	2350
MS	PCG	${10}^{-1}$	1	${10}^{-1}$	$1.07\times {10}^{-03}$	$1.91\times {10}^2$	$1.79\times {10}^5$	557
MS	PCG	${10}^{-2}$	1	${10}^{-2}$	$1.07\times {10}^{-02}$	$1.19\times {10}^3$	$1.12\times {10}^5$	416
MS	PCG	${10}^{-3}$	1	${10}^{-3}$	$1.06\times {10}^{-01}$	$1.19\times {10}^4$	$1.12\times {10}^5$	606
MS	PCG	${10}^{-4}$	1	${10}^{-4}$	$4.86\times {10}^{-01}$	$1.19\times {10}^5$	$2.45\times {10}^5$	1254
MS	PCG	${10}^{-5}$	1	${10}^{-5}$	$4.86\times {10}^{-01}$	$1.19\times {10}^6$	$2.45\times {10}^6$	2367
MS	DPCG (1)	1	1	1	$1.09\times {10}^{-04}$	6.44	$5.93\times {10}^4$	294
MS	DPCG (1)	1	${10}^5$	${10}^{-5}$	$1.09\times {10}^{-04}$	6.44	$5.92\times {10}^4$	293
MS	DPCG (5)	1	1	1	$1.07\times {10}^{-04}$	6.44	$6.03\times {10}^4$	342
MS	DPCG (5)	1	${10}^1$	${10}^{-1}$	$1.07\times {10}^{-04}$	6.44	$6.03\times {10}^4$	331
MS	DPCG (5)	1	${10}^2$	${10}^{-2}$	$1.07\times {10}^{-04}$	6.44	$6.04\times {10}^4$	385
MS	DPCG (5)	1	${10}^3$	${10}^{-3}$	$1.06\times {10}^{-04}$	6.44	$6.05\times {10}^4$	544
MS	DPCG (5)	1	${10}^4$	${10}^{-4}$	$4.96\times {10}^{-05}$	6.44	$1.30\times {10}^5$	961
MS	DPCG (5)	1	${10}^5$	${10}^{-5}$	$4.95\times {10}^{-06}$	6.44	$1.30\times {10}^6$	1456
Liu	PCG	1	1	1	$1.06\times {10}^{-04}$	$6.98\times {10}^1$	$6.56\times {10}^5$	1401
Liu	PCG	1	${10}^1$	${10}^{-1}$	$1.06\times {10}^{-04}$	$1.19\times {10}^1$	$1.12\times {10}^5$	561
Liu	PCG	1	${10}^2$	${10}^{-2}$	$1.06\times {10}^{-04}$	$1.19\times {10}^1$	$1.12\times {10}^5$	563
Liu	PCG	1	${10}^3$	${10}^{-3}$	$5.91\times {10}^{-05}$	$1.19\times {10}^1$	$2.02\times {10}^5$	1154
Liu	DPCG (5)	1	1	1	$1.07\times {10}^{-04}$	6.44	$6.05\times {10}^4$	419
Liu	DPCG (5)	1	${10}^1$	${10}^{-1}$	$1.07\times {10}^{-04}$	6.44	$6.05\times {10}^4$	399
Liu	DPCG (5)	1	${10}^2$	${10}^{-2}$	$1.06\times {10}^{-04}$	6.44	$6.05\times {10}^4$	520
Liu	DPCG (5)	1	${10}^3$	${10}^{-3}$	$6.02\times {10}^{-05}$	6.44	$1.07\times {10}^5$	1046

${}^{\mathrm{a}}$MS = ssSNPBLUP model proposed by Mantysaari and Stranden [7]; Liu = ssSNPBLUP model proposed by Liu et al. [5]

${}^{\mathrm{b}}$Number of SNP effects per subdomain is within brackets

${}^{\mathrm{c}}$Parameters used for the second-level preconditioner $\mathbf{D}$

${}^{\mathrm{d}}$Smallest and largest eigenvalues of the preconditioned (deflated) coefficient matrix

${}^{\mathrm{e}}$Condition number of the preconditioned (deflated) coefficient matrix

${}^{\mathrm{f}}$Number of iterations. A number of iterations equal to 10,000 means that the method failed to converge within 10,000 iterations