Research Article
A New Modified Levenberg–Marquardt Method for Systems of Nonlinear Equations
Table 5
Results on the first singular test set with
.
| Function | | | NF/NJ/NJ NF | | | | | |
| Rosenbrock | 2 | 1 | 15/15/45 | 15/15/45 | 15/15/45 | 19/17/53 | 153/80/313 | 10 | 17/17/51 | 17/17/51 | 18/18/54 | 143/75/293 | 185/96/377 | 100 | 20/20/60 | 21/21/63 | 23/22/67 | 130/68/266 | — |
| Powell singular | 4 | 1 | 10/10/50 | 10/10/50 | 10/10/50 | 10/10/50 | 10/10/50 | 10 | 13/13/65 | 13/13/65 | 13/13/65 | 13/13/65 | 17/17/85 | 100 | 16/16/80 | 16/16/80 | 16/16/80 | 20/20/100 | 106/106/530 |
| Wood | 4 | 1 | 16/16/80 | 16/16/80 | 16/16/80 | 16/16/80 | 17/17/85 | 10 | 19/19/95 | 19/19/95 | 19/19/95 | 20/20/100 | 26/26/130 | 100 | 22/22/110 | 22/22/110 | 22/22/110 | 26/26/130 | — |
| Helical valley | 3 | 1 | 8/8/32 | 8/8/32 | 8/8/32 | 8/8/32 | 9/9/36 | 10 | 8/8/32 | 8/8/32 | 8/8/32 | 9/9/36 | 10/10/40 | 100 | 8/8/32 | 8/8/32 | 8/8/32 | 9/9/36 | 12/12/48 |
| Brown almost: linear | 10 | 1 | 8/8/88 | 8/8/88 | 8/8/88 | 8/8/88 | 8/8/88 | 10 | 23/23/253 | 23/23/253 | 23/23/253 | 28/28/308 | — | 100 | 45/45/495 | 45/45/495 | 45/45/495 | — | — |
| Discrete boundary value | 10 | 1 | 3/3/33 | 4/4/44 | 4/4/44 | 4/4/44 | 4/4/44 | 10 | 7/7/77 | 7/7/77 | 8/8/88 | 8/8/88 | 8/8/88 | 100 | 9/9/99 | 9/9/99 | 9/9/99 | 9/9/99 | 10/10/110 |
| Discrete integral equation | 30 | 1 | 6/6/186 | 6/6/186 | 6/6/186 | 6/6/186 | 6/6/186 | 10 | 7/7/217 | 7/7/217 | 7/7/217 | 7/7/217 | 6/6/186 | 100 | 10/10/310 | 10/10/310 | 10/10/310 | 11/11/341 | 14/14/434 |
| Trigonometric | 30 | 1 | 25/17/535 | 29/19/599 | 34/18/574 | 37/17/547 | 30/9/300 | 10 | 56/38/1196 | 60/41/1290 | 59/42/1319 | 69/40/1269 | 57/28/897 | 100 | 41/35/1091 | 36/22/696 | 43/25/793 | 46/24/766 | 48/23/738 |
| Variably dimensioned | 10 | 1 | 14/14/154 | 14/14/154 | 14/14/154 | 14/14/154 | 18/18/198 | 10 | 16/16/176 | 16/16/176 | 16/16/176 | 17/17/187 | 23/23/253 | 100 | 19/19/209 | 19/19/209 | 19/19/209 | 25/25/275 | — |
| Broyden tridiagonal | 30 | 1 | 9/9/279 | 9/9/279 | 9/9/279 | 9/9/279 | 9/9/279 | 10 | 14/14/434 | 14/14/434 | 14/14/434 | 14/14/434 | 17/17/527 | 100 | 17/17/527 | 17/17/527 | 17/17/527 | 21/21/651 | 85/85/2635 |
| Broyden banded | 30 | 1 | 12/12/372 | 12/12/372 | 12/12/372 | 12/12/372 | 12/12/372 | 10 | 18/18/558 | 18/18/558 | 18/18/558 | 21/21/651 | 30/30/930 | 100 | 24/24/744 | 24/24/744 | 24/24/744 | 34/34/1054 | — |
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