Jason Shepherd

LaTeX experiment

Posted by jbshep on May 5, 2011

I read that WordPress supports LaTeX, so let’s try this out. Here is the 1-D interval Newton’s method.

$X_{n+1} = \left[ m(X_n) - \dfrac{f(m(X_n))}{f^{\prime}(X_n)} \right] \cap X_n$

where $X_n, X_{n+1} \in \mathbb{IR}$ and $m(X_n) = ( \underline{X_n} + \overline{X_{n+1}})/2$

Cool! Now let’s try the Jacobian matrix:

$J_f = \begin{bmatrix} \frac{\partial f_1}{\partial x_1} &\frac{\partial f_1}{\partial x_2} &\hdots &\frac{\partial f_1}{\partial x_n} \\ \frac{\partial f_2}{\partial x_1} &\frac{\partial f_2}{\partial x_2} &\hdots &\hdots \\ \vdots &\vdots &\ddots &\hdots \\ \frac{\partial f_n}{\partial x_1} &\hdots &\hdots &\frac{\partial f_n}{\partial x_n} \end{bmatrix}$