Condition number of system of non-linear equations. The system has only two unknowns but 6 equations (thus over-determined). Solving the system of equations are not a problem. However, I need an indication of how well-conditioned the system of equations is. I know the condition number is typically used to do this. Any advice on exactly how this procedure works will be appreciated.

Question

knolsaadme · Accepted Answer

Let say that you have   N equations for   M unknowns (  N  &amp;gt;  M). You can consider minimizing of the norm  Φ  (      x    1    ,      x    2    ,      x    3    ,  .  .  ,      x    M    )  =      ∑          i      =      1        N        g    i    (      x    1    ,      x    2    ,      x    3    ,  .  .  ,      x    M        )    2  hoping that at solution   Φ will be zero. The Jacobian of the system leads to a square   M  ×  Msystem.