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# 62. mnewton

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## 62.1 Functions and Variables for mnewton

Option variable: newtonepsilon

  Default value: `10.0^(-fpprec/2)`

  Precision to determine when the `mnewton` function has converged towards the solution.

  See also `mnewton`.

Option variable: newtonmaxiter

  Default value: `50`

  Maximum number of iterations to stop the `mnewton` function if it does not converge or if it converges too slowly.

  See also `mnewton`.

Function: mnewton (FuncList,VarList,GuessList)

  Multiple nonlinear functions solution using the Newton method. FuncList is the list of functions to solve, VarList is the list of variable names, and GuessList is the list of initial approximations.

  The solution is returned in the same format that `solve()` returns. If the solution isn't found, `[]` is returned.

  This function is controlled by global variables `newtonepsilon` and `newtonmaxiter`.

      (%i1) load("mnewton")$

      (%i2) mnewton([x1+3*log(x1)-x2^2, 2*x1^2-x1*x2-5*x1+1],
                    [x1, x2], [5, 5]);
      (%o2) [[x1 = 3.756834008012769, x2 = 2.779849592817897]]
      (%i3) mnewton([2*a^a-5],[a],[1]);
      (%o3)             [[a = 1.70927556786144]]
      (%i4) mnewton([2*3^u-v/u-5, u+2^v-4], [u, v], [2, 2]);
      (%o4) [[u = 1.066618389595407, v = 1.552564766841786]]

  To use this function write first `load("mnewton")`. See also `newtonepsilon` and `newtonmaxiter`.

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