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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

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

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