Table 2.

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

${\text{Model}}^{\mathrm{a}}$	Method	$k_O/k_S^{\mathrm{b}}$	${\lambda }_{\mathit{min}}^{\mathrm{c}}$	${\lambda }_{\mathit{max}}^{\mathrm{c}}$	${\kappa }^{\mathrm{d}}$	${\mathit{N}}^{\mathrm{e}}$	$\text{Iterative}{\text{time}}^{\mathrm{f}}$	${\text{Time/iter.}}^{\mathrm{g}}$	$\text{Total}{\text{time}}^{\mathrm{h}}$
MS	PCG	1	$3.70\times {10}^{-5}$	$1.75\times {10}^3$	$4.74\times {10}^7$	10,000	44,808	4.5	46,081
MS	PCG	${10}^{-1}$	$1.18\times {10}^{-5}$	$1.77\times {10}^2$	$1.51\times {10}^7$	10,000	51,768	5.2	53,550
MS	PCG	${10}^{-2}$	$4.37\times {10}^{-6}$	$1.95\times {10}^1$	$4.45\times {10}^6$	6210	34,139	5.5	35,812
MS	PCG	${10}^{-3}$	$3.99\times {10}^{-6}$	5.08	$1.27\times {10}^6$	3825	19,043	5.0	20,866
MS	PCG	${10}^{-4}$	$1.50\times {10}^{-6}$	5.07	$3.37\times {10}^6$	7336	54,326	7.4	56,475
MS	DPCG	1	$2.86\times {10}^{-5}$	4.77	$1.67\times {10}^5$	748	6527	8.7	17,229
MS	DPCG	${10}^{-1}$	$1.41\times {10}^{-5}$	4.77	$3.37\times {10}^5$	1211	11,864	9.8	22,947
MS	DPCG	${10}^{-2}$	$9.17\times {10}^{-6}$	4.77	$5.20\times {10}^5$	1778	17,030	9.6	28,615
MS	DPCG	${10}^{-3}$	$7.50\times {10}^{-6}$	4.77	$6.36\times {10}^5$	2569	23,676	9.2	35,497
Liu	PCG	1	$7.38\times {10}^{-6}$	$1.43\times {10}^2$	$1.93\times {10}^7$	10,000	44,122	4.4	45,083
Liu	PCG	${10}^{-1}$	$3.66\times {10}^{-6}$	$1.52\times {10}^1$	$4.14\times {10}^6$	6049	31,085	5.1	32,018
Liu	PCG	${10}^{-2}$	$4.29\times {10}^{-6}$	5.07	$1.18\times {10}^6$	2669	13,225	5.0	13,888
Liu	PCG	${10}^{-3}$	$3.51\times {10}^{-6}$	5.07	$1.44\times {10}^6$	3606	20,578	5.7	21,458
Liu	PCG	${10}^{-4}$	$1.69\times {10}^{-6}$	5.07	$3.00\times {10}^6$	7033	33,534	4.8	34,675
Liu	DPCG	1	$5.40\times {10}^{-6}$	5.31	$9.85\times {10}^5$	2877	22,791	7.9	26,521
Liu	DPCG	${10}^{-1}$	$6.91\times {10}^{-6}$	4.77	$6.90\times {10}^5$	1628	14,231	8.7	18,049
Liu	DPCG	${10}^{-2}$	$5.23\times {10}^{-6}$	4.77	$9.11\times {10}^5$	2234	23,244	10.4	28,057
Liu	DPCG	${10}^{-3}$	$4.31\times {10}^{-6}$	4.77	$1.11\times {10}^6$	3106	34,950	11.3	39,603

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

${}^{\mathrm{b}}$Parameters used for the second-level preconditioner;

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

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

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

${}^{\mathrm{f}}$Wall clock time (seconds) for the iterative process;

${}^{\mathrm{g}}$Average wall clock time (seconds) per iteration;

${}^{\mathrm{h}}$Wall clock time (seconds) for a complete process (including I/O operations)