Brenden Tran

2022-06-26

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.

Expert

Let say that you have $N$ equations for $M$ unknowns ($N>M$). You can consider minimizing of the norm
$\mathrm{\Phi }\left({x}_{1},{x}_{2},{x}_{3},..,{x}_{M}\right)=\sum _{i=1}^{N}{g}_{i}\left({x}_{1},{x}_{2},{x}_{3},..,{x}_{M}{\right)}^{2}$
hoping that at solution $\mathrm{\Phi }$ will be zero. The Jacobian of the system leads to a square $M×M$system.

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