Finding extremum of Rosenbrock's function:

Newton's method with numerical jacobian:
initial vector xo:          5         10 
            f(xo):  3.001e+04      -3000 
       solution x:          1          1 
             f(x):  8.855e-08 -4.253e-08 
            calls:  4178
             time:  1.371

Newton's method with analytic jacobian:
initial vector xo:          5         10 
            f(xo):  3.001e+04      -3000 
       solution x:          1          1 
             f(x):  8.625e-08 -4.197e-08 
            calls:  3749
             time:  1.245

Finding roots of fA(x,y) = {Axy-1, exp(-x)+exp(-y)-1-1/A} :

Newton's method with numerical jacobian:
initial vector xo:          2          1 
           fA(xo):      2e+04    -0.4969 
       solution x:      9.106  1.098e-05 
            fA(x): -8.706e-06  5.428e-08 
            calls:  43
             time:  0.014

Newton's method with analytic jacobian:
initial vector xo:          2          1 
           fA(xo):      2e+04    -0.4969 
       solution x:      9.106  1.098e-05 
            fA(x): -8.706e-06  5.426e-08 
            calls:  33
             time:  0.011