#
#  Program for the fixed iteration
#      x[k] = g(x[k-1])
#
#  Input:     g --- the function as an operator
#            x0 --- the initial iterate
#             N --- the maximum steps allowed
#           tol --- the error tolerance
#
fixed_it:=proc(   g::operator,
                 x0::numeric,
                  N::integer,
                tol::numeric
               )
   local x, k;

   x:=array(0..N);
   x[0]:=x0;

   for k from 1 to N do

      x[k]:= g(x[k-1]);
      print( k, x[k], abs( x[k]-x[k-1])  );

      # stopping criterion
      if abs(x[k]-x[k-1])<tol then
         print(`The solution`,x[k]); 
         RETURN();
      fi

   od;

   print(`The iteration failed`);

end;