I'm not great at maths so go easy.
I'm following this video on how to solve a problem in which repeated guesses are taken at the inputs, $x_{1-6}$, of a function $f(x_1,x_2,x_3,x_4,x_5,x_6)$ and the output, a vector $y = f(x_{1-6})$ is used to determine the next iteration. $y0$ the desired output is known.
To determine the next guess, $x_{1-6_2}$, the numerical Jacobian $J = (f(x_{1-6}+e) - f(x_{1-6}))/e$ is calculated. With $dy = y0 - y$, $dx =J^+\,dy$ gives the next iteration of guesses $x_{1-6}$: $x_{n+1} = x_n+dx$.
This $dx =J^+\,dy$, gives the values for $dx$ that is the least square solution for $J\,dx = dy$.
So my confusion is about the Jacobian and why it's used here. Why does finding the values of $dx$ that minimises the least square $J\,dx = dy$ give guesses that incrementally move $x$ to the correct answer?
Also would it be more accurate of those '$d$'s were partial derivatives?
Thanks, I'm trying to understand this so I can give an explanation of it to other engineers.