Jason Shepherd

Jason Shepherd http://jbshep.wordpress.com from cerebral ephemera to digital permanence Thu, 05 May 2011 02:00:52 +0000 en hourly 1 http://wordpress.com/ http://s2.wp.com/i/buttonw-com.png Jason Shepherd http://jbshep.wordpress.com LaTeX experiment http://jbshep.wordpress.com/2011/05/05/latex-experiment/ http://jbshep.wordpress.com/2011/05/05/latex-experiment/#comments Thu, 05 May 2011 00:50:42 +0000 jbshep http://jbshep.wordpress.com/?p=41 ]]> 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:

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

Wow. This is nice!

]]> http://jbshep.wordpress.com/2011/05/05/latex-experiment/feed/ 0 jbshep First palindrome! (Emordnilaptsrif!) http://jbshep.wordpress.com/2011/03/26/first-palindrome-emordnilaptsrif/ http://jbshep.wordpress.com/2011/03/26/first-palindrome-emordnilaptsrif/#comments Sat, 26 Mar 2011 13:11:36 +0000 jbshep http://jbshep.wordpress.com/?p=35 ]]> A man, a plan, a canal, panama….

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