| LU and QR factorizations | 2.4, 2.5, 3.2, 3.3, 3.5, 4.1, 4.2, 5.1-5.4, 5.6 |
|---|---|
| SVD, norms and LSQ | 6.1, 6.3, 7.1-7.4, 8.1-8.3, 9.1-9.3, 9.4.1 |
| Kronecker products | 10.1, 10.2, 10.3, 11.1, 11.2, 11.3 |
| Iterative methods | 12.1-12.4, 13.1-13.3, 13.5 |
| Eigenpairs | 14.1-14.5, 15.1-15.3 |
columns: LU and QR factorizations | 2.4, 2.5, 3.2, 3.3, 3.5, 4.1, 4.2, 5.1-5.4, 5.6
| \(k_{100}\) | \(k_{2500}\) | \(k_{10} 000\) | \(k_{40000}\) | \(k_{160} 000\) | |
|---|---|---|---|---|---|
| J | 385 | 8386 | |||
| GS | 194 | 4194 | |||
| SOR | 35 | 164 | 324 | 645 | 1286 |
columns: | \(k_{100}\) | \(k_{2500}\) | \(k_{10} 000\) | \(k_{40000}\) | \(k_{160} 000\)
| \(\mathrm{n}=100\) | \(\mathrm{n}=2500\) | \(k_{100}\) | \(k_{2500}\) | |
|---|---|---|---|---|
| J | 0.959493 | 0.998103 | 446 | 9703 |
| GS | 0.920627 | 0.99621 | 223 | 4852 |
| SOR | 0.56039 | 0.88402 | 32 | 150 |
columns: | \(\mathrm{n}=100\) | \(\mathrm{n}=2500\) | \(k_{100}\) | \(k_{2500}\)
| \(n\) | 2500 | 10000 | 40000 | 1000000 | 4000000 |
|---|---|---|---|---|---|
| \(K\) | 19 | 18 | 18 | 16 | 15 |
columns: \(n\) | 2500 | 10000 | 40000 | 1000000 | 4000000
| \(n\) | 2500 | 10000 | 40000 | 160000 |
|---|---|---|---|---|
| \(K\) | 94 | 188 | 370 | 735 |
| \(K / \sqrt{n}\) | 1.88 | 1.88 | 1.85 | 1.84 |
columns: \(n\) | 2500 | 10000 | 40000 | 160000
| \(n\) | 2500 | 10000 | 22500 | 40000 | 62500 |
|---|---|---|---|---|---|
| \(K\) | 222 | 472 | 728 | 986 | 1246 |
| \(K / \sqrt{n}\) | 4.44 | 4.72 | 4.85 | 4.93 | 4.98 |
| \(K_{\text {pre }}\) | 22 | 23 | 23 | 23 | 23 |
columns: \(n\) | 2500 | 10000 | 22500 | 40000 | 62500
| \(k\) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| \(\|\boldsymbol{r}\|_{2}\) | \(1.0 \mathrm{e}+000\) | 7.7e-002 | 1.6e-004 | 8.2e-010 | 2.0e-020 |
| \(\left|s-\lambda_{1}\right|\) | 3.7e-001 | -1.2e-002 | -2.9e-005 | -1.4e-010 | -2.2e-016 |
columns: \(k\) | 1 | 2 | 3 | 4 | 5