I'm studying Advanced motion control and we use Newton's method for iterative optimisation to find the minimum (optimal) control input. So my question is, Consider the following iterative update algorithm applied to find the minimum of
a function f(u), $$u(k+1)= u(k)- \frac{\frac{df}{du}}{\frac{d^2f}{du^2}}$$
If f(u) is a quadratic, prove that the above algorithm will cause u to
reach the optimal function input,u*, in one step from any initial condition.
2026-03-29 17:31:12.1774805472
How to prove that Newton's method for optimization will converge in one step
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