Table 2 Characteristics of preconditioned (deflated) coefficient matrices, and of PCG and DPCG methods for solving ssSNPBLUP applied to the field dataset
From: A second-level diagonal preconditioner for single-step SNPBLUP
\(\text{Model}^{\mathrm{a}}\) | Method | \(k_{O}/k_{S}^{\mathrm{b}}\) | \(\lambda _{min}^{\mathrm{c}}\) | \(\lambda _{max}^{\mathrm{c}}\) | \(\kappa ^{\mathrm{d}}\) | \(\textit{N}^{\mathrm{e}}\) | \(\text{Iterative time}^{\mathrm{f}}\) | \(\text{Time/iter.}^{\mathrm{g}}\) | \(\text{Total time}^{\mathrm{h}}\) |
|---|---|---|---|---|---|---|---|---|---|
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 |