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	—