Theory and Modern Applications
Table 3 Residual errors of simultaneous methods PJM10D, MNS10D, MNS10M, MNS12D and MNS12M for finding all the distinct as well as multiple roots of polynomial equation used in Example 2
From: Efficient iterative methods for finding simultaneously all the multiple roots of polynomial equation
Method | CO | n | CPU | \({ e}_{1}\) | \({ e} _{2}\) | \({ e}_{3}\) | \({ e}_{4}\) | \({ e}_{5}\) | \({ e}_{6}\) | \({ e}_{7}\) | \({ e}_{8}\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
PJM10D | 10 | 2 | 0.594 | 1.2e-1 | 3.0e-2 | 2.7e-1 | 7.9e-2 | 1.8e-1 | 3.1e-2 | 1.2e-1 | 8.2e-3 |
MNS10D | 10 | 2 | 0.25 | 5.6e-62 | 3.9e-59 | 0.0 | 5.3e-58 | 1.2e-62 | 2.0e-58 | 1.8e-63 | 4.2e-59 |
MNS10M | 10 | 2 | 0.65 | 9.1e-115 | 3.9e-174 | 0.0 | 1.0e-113 | 1.4e-120 | 1.7e-114 | 6.7e-193 | 10e-113 |
MNS12D | 12 | 2 | 0.343 | 4.2e-64 | 1.2e-65 | 0.0 | 0.0 | 1.3e-71 | 1.7e-64 | 3.1e-67 | 0.0 |
MNS12M | 12 | 2 | 0.282 | 1.1e-113 | 5.0e-177 | 0.0 | 2.3e-121 | 6.7e-125 | 6.6e-114 | 6.5e-197 | 5.4e-121 |