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

Table 2

Results of Algorithm 1 for Powell singular function with initial point , stopping criterion , with (left), (middle), (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	2.8290e + 01	3.1722e + 00	2	2.8288e + 01	3.1723e + 00	2	2.8270e + 01	3.1744e + 00
3	3.5362e + 00	7.9304e − 01	3	3.5364e + 00	7.9308e − 01	3	3.5389e + 00	7.9361e − 01
4	4.4203e − 01	1.9826e − 01	4	4.4205e − 01	1.9827e − 01	4	4.4240e − 01	1.9840e − 01
5	5.5254e − 02	4.9565e − 02	5	5.5257e − 02	4.9568e − 02	5	5.5300e − 02	4.9601e − 02
6	6.9067e − 03	1.2391e − 02	6	6.9072e − 03	1.2392e − 02	6	6.9125e − 03	1.2400e − 02
7	8.6335e − 04	3.0978e − 03	7	8.6340e − 04	3.0980e − 03	7	8.6407e − 04	3.1001e − 03
8	1.0792e − 04	7.7446e − 04	8	1.0792e − 04	7.7450e − 04	8	1.0801e − 04	7.7502e − 04
9	1.3490e − 05	1.9362e − 04	9	1.3491e − 05	1.9362e − 04	9	1.3501e − 05	1.9375e − 04
10	1.6862e − 06	4.8405e − 05	10	1.6863e − 06	4.8406e − 05	10	1.6876e − 06	4.8439e − 05