Condition number of system of non-linear equations. The system has only two unknowns but 6...

Brenden Tran

Brenden Tran

Answered

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.

Answer & Explanation

knolsaadme

knolsaadme

Expert

2022-06-27Added 16 answers

Let say that you have N equations for M unknowns ( N > 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.

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