# How to solve a nonlinear overdetermined system of equations

i'm trying to solve a nonlinear overdetermined system of equations (124 equations, 123 variables) i tried this procedure (newton raphson)

NewtonExtended[f_List, x_List, x0_List, eps_: 10^-12, n_: 100] := With[{jac = N[Outer[D, f, x]]}, FixedPoint[(# + PseudoInverse[ jac /. Thread[x -> N[#]]].(-f /. Thread[x -> N[#]])) &, N[x0], n, SameTest -> (Sqrt[Abs[(#1 - #2).(#1 - #2)]] < eps &)]]

but it takes so long (without giving any solution) because i'm using a signal of 300 samples (need to use it 300 times), i need a procedure to be quick and gives the solution in a reasonable time

• Why not reformulate as an optimization problem that you can give to FindMinimum[]/NMinimize[]? – J. M. will be back soon Jul 6 '15 at 12:38
• @Guesswhoitis. i don't know how to use it properly – El Amraoui Abdelilah Jul 11 '15 at 2:10
• Treat each equation as a component in the sum of squares that you'll be minimizing. – J. M. will be back soon Jul 11 '15 at 2:29