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

Table 6

Results on the first high-dimensional singular test set with .

Function			NF/NJ/NJ NF
			Brown almost: linear	500	1	9/9/4509	9/9/4509	9/9/4509	10/10/5010	12/12/6012
Discrete boundary value	500	1	1/1/501	1/1/501	1/1/501	1/1/501	1/1/501
		10	5/5/2505	3/3/1503	3/3/1503	3/3/1503	3/3/1503
		100	10/10/5010	9/9/4509	9/9/4509	9/9/4509	9/9/4509
Discrete integral equation	1000	1	7/7/7007	7/7/7007	7/7/7007	7/7/7007	7/7/7007
		10	8/8/8008	8/8/8008	7/7/7007	10/10/10010	11/11/11011
		100	10/10/10010	10/10/10010	10/10/10010	12/12/12012	17/17/17017
Trigonometric	1000	1	13/8/8013	18/9/9018	22/8/8022	25/8/8025	29/9/9029
		10	30/21/21030	33/19/19033	41/25/25041	40/18/18040	40/18/18040
		100	35/23/23035	38/27/27038	67/38/38067	65/38/38065	69/37/37069
Variably dimensioned	500	1	28/28/14028	28/28/14028	28/28/14028	179/179/89679	—
		10	30/30/15030	30/30/15030	30/30/15030	3266/3266/1636266	—
		100	34/34/17034	34/34/17034	34/34/17034	—	—
Broyden tridiagonal	1000	1	9/9/9009	9/9/9009	9/9/9009	9/9/9009	9/9/9009
		10	14/14/14014	14/14/14014	14/14/14014	16/16/16016	20/20/20020
		100	17/17/17017	17/17/17017	17/17/17017	23/23/23023	1972/1972/1973972
Broyden banded	1000	1	12/12/12012	12/12/12012	12/12/12012	12/12/12012	13/13/13013
		10	18/18/18018	18/18/18018	18/18/18018	22/22/22022	178/178/178178
		100	24/24/24024	24/24/24024	24/24/24024	77/77/77077	—