# Newton Raphson method initial guess

I am facing problems in making the initial guess while applying Newton-Raphson method to equations of more than one variable.Is ther some thumb rule for making the initial guess in the general case?To be specific let the system of equations be $$f_i(x,y,w,z) ,i=1,2,3,4$$,where all the four functions are algebraic functions.Thanks for any help in advance .

• Can you provide an actual set of equations to solve? – Moo Aug 5 '17 at 5:36
• As Moo commented, it would be good to know the equations. Let me play with them. – Claude Leibovici Aug 5 '17 at 9:18

One thing you can consider if $$\Phi(x,y,w,z)=\sum_{i=1}^4 f^2_i(x,y,w,z)$$ which should be zero at the solution.
So, and this is a thing I use to do, compute $\Phi(x,y,w,z)$ over a four dimension grid and select as a starting point the point corresponding to the minimum value you noticed.