IK: Numerical methods

Numerical inversion of \(p=f(\theta)\), \(\theta=(\theta_0,\cdots,\theta_{N-1})\).

• Consider small step size \(p\to p+\Delta p\)
• \(\displaystyle \Delta p \simeq \underbrace{\left( \frac{\partial f}{\partial \theta}\right)}_{\mathrm{J}}\;\Delta \theta\)

• \(J\) - Jacobian matrix.
• \(\rightarrow\) Not square (\(3\times N\)), not invertible.