Theory and Modern Applications
Table 2 Residual errors of simultaneous methods PJM10D, MNS10D and MNS12D for finding all the distinct roots of polynomial equation used in Example 1
From: Efficient iterative methods for finding simultaneously all the multiple roots of polynomial equation
Method | CO | n | CPU | \({e}_{1} \) | \({e}_{2}\) | \({e}_{3}\) | \({e}_{4}\) | \({e}_{5}\) | \({e}_{6}\) | \({e}_{7}\) | e8 | \({e}_{9}\) | \({e}_{10}\) | \({e}_{11}\) | \({e}_{12}\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
PJM10D | 10 | 3 | 1.234 | 1.7e-4 | 8.6e-5 | 3.4e-5 | 2.5e-4 | 1.2e-3 | 2.4e-4 | 3.5e-4 | 1.2e-5 | 113.9e-0 | 209.0e-0 | 8.8e-4 | 2.8e-4 |
MNS10D | 10 | 3 | 0.656 | 1.8e-36 | 5.8e-39 | 5.0e-41 | 1.6e-22 | 1.1e-21 | 7.5e-45 | 8.8e-30 | 7.3e-46 | 3.5e–4 | 1.6e-3 | 1.9e-33 | 3.6e-59 |
MNS12D | 12 | 3 | 0.563 | 1.4e-60 | 2.2e-62 | 0.0 | 0.0 | 3.0e-63 | 1.0e-62 | 2.2e-62 | 0.0 | 9.2e-62 | 1.2e-58 | 1.0e-59 | 1.4e-59 |