(maxima.info)Functions and Variables for mnewton

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73.2 Functions and Variables for mnewton
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 -- Option variable: newtonepsilon
     Default value: '10.0^(-fpprec/2)'

     Precision to determine when the 'mnewton' function has converged
     towards the solution.  If 'newtonepsilon' is a bigfloat, then
     'mnewton' computations are done with bigfloats.  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 is not 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]]

     The variable 'newtonepsilon' controls the precision of the
     approximations.  It also controls if computations are performed
     with floats or bigfloats.

          (%i1) load(mnewton)$

          (%i2) (fpprec : 25, newtonepsilon : bfloat(10^(-fpprec+5)))$

          (%i3) mnewton([2*3^u-v/u-5, u+2^v-4], [u, v], [2, 2]);
          (%o3) [[u = 1.066618389595406772591173b0,
                                         v = 1.552564766841786450100418b0]]

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