% m20_newtonsystem.m - Newton's method for system of two equations
%     More robust codes in Matlab: help optim, help fzero, help fsolve

  format compact, format long
  x = [0; 0]
  for k = 0:5
    pause

    F = [ sin(x(1)+x(2)) - exp(-x(1)^2) 
             3*x(1) - x(1)*x(2)^2 - 1   ] ;

    J = [ cos(x(1)+x(2)) + 2*x(1)*exp(-x(1)^2)    cos(x(1)+x(2))
                 3 - x(2)^2                        -2*x(1)*x(2)   ] ;

    s = -J\F;
    x = x + s         
  end