# Second order Taylor method to address system of formulas

How do I make use of 2nd order Taylor method to address a system of non - straight formulas? Exists an excellent reference that offers information? I located states of it in a loads of mathematical evaluation publications, yet no instances

Specifically, $f:\mathbb{R}^n \to \mathbb{R}^m$, address $f(\mathbf{x})=\mathbf{0}$ making use of 2nd order Taylor development of $f$ around first hunch $\mathbf{x_0}$

One means to address $f(x) = y$ is to decrease $g(x) = (f(x) - y)^2$. You can do this by taking the square estimate to $g(x)$ that originates from the 2nd order Taylor collection focused at your first hunch, locating its minimum, and also allowing that minimum be the beginning hunch for the next model. This isn't always the most effective algorithm, yet it is understandable and also implement.

For high - dimensional troubles, the job remains in addressing the system of formulas to decrease the square estimate. A large amount of study has actually entered into doing that action intelligently, capitalizing on thin matrix framework etc

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