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

Table 1

Results for Powell singular function with initial point , stopping criterion , with (left), (middle), and (right).

Iters		Function	Iters		Function	Iters		Function
1	2.2939e + 02	1.4663e + 01	1	2.2939e + 02	1.4663e + 01	1	2.2939e + 02	1.4663e + 01
2	2.7810e + 01	3.3467e + 00	2	3.1599e + 01	4.4743e + 00	2	9.1950e + 01	8.7473e + 00
3	3.4658e + 00	9.9547e − 01	3	4.6835e + 00	2.3177e + 00	5	4.0764e + 00	2.5941e + 00
6	9.8048e − 02	1.4095e − 01	7	9.2544e − 02	1.3340e − 01	8	5.9456e − 01	5.3381e − 01
14	9.9650e − 03	2.9959e − 02	10	5.0828e − 03	1.8397e − 02	10	4.0460e − 02	7.8054e − 02
48	9.6615e − 04	6.2663e − 03	13	4.8857e − 04	3.8486e − 03	13	2.5177e − 04	1.9426e − 03
197	9.9776e − 05	1.3761e − 03	16	7.5193e − 05	1.1112e − 03	14	3.8748e − 05	5.1794e − 04
888	9.9937e − 06	2.9662e − 04	21	6.8285e − 06	2.2647e − 04	15	5.5404e − 06	1.3449e − 04