A New Modified Levenberg–Marquardt Method for Systems of Nonlinear Equations

Table 7

Results on the second singular test set with .

Function			NF/NJ/NJ NF
			Rosenbrock	2	1	11/11/33	11/11/33	11/11/33	11/11/33	11/11/33
10	13/13/39	13/13/39			13/13/39	14/14/42	18/18/54
100	17/17/51	17/17/51			17/17/51	20/20/60	133/133/399
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	14/14/70	14/14/70	14/14/70	14/14/70	15/15/75
		10	17/17/85	17/17/85	17/17/85	19/19/95	24/24/120
		100	20/20/100	20/20/100	20/20/100	26/26/130	—
Helical valley	3	1	13/13/52	13/13/52	13/13/52	13/13/52	13/13/52
		10	14/14/56	14/14/56	14/14/56	12/12/48	15/15/60
		100	14/14/56	14/14/56	16/15/61	82/44/214	29/23/98
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	10/10/110	10/10/110	10/10/110	10/10/110	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	15/15/465
Trigonometric	30	1	18/12/378	21/10/321	24/11/354	29/10/329	31/11/361
		10	37/25/787	63/41/1293	58/39/1228	81/45/1431	49/30/949
		100	89/66/2069	57/41/1287	44/31/974	39/21/669	50/25/800
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	—