Table 1 Characteristics of preconditioned (deflated) coefficient matrices, and of PCG and DPCG methods for solving ssSNPBLUP applied to the reduced dataset
From: A second-level diagonal preconditioner for single-step SNPBLUP
| \(\text{Model}^{\mathrm{a}}\) | \(\text{Method}^{\mathrm{b}}\) | \(k_{O}^{\mathrm{c}}\) | \(k_{S}^{\mathrm{c}}\) | \(k_{O}/k_{S}\) | \(\lambda _{min}^{\mathrm{d}}\) | \(\lambda _{max}^{\mathrm{d}}\) | \(\kappa ^{\mathrm{e}}\) | \(\textit{N}^{\mathrm{f}}\) |
|---|---|---|---|---|---|---|---|---|
| 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 |