#+ -*- coding: iso-8859-1; -*-
#+TITLE:     Numerical methods with Octave
#+AUTHOR:    Eric S Fraga
#+EMAIL:     address@hidden
#+DATE:      2010.10.10 18:54:55

* COMMENT Preamble						   :noexport:
#+DESCRIPTION: 
#+KEYWORDS: 
#+LANGUAGE:  en
#+OPTIONS:   H:3 num:t toc:nil \n:nil @:t ::t |:t ^:t -:t f:t *:t <:t
#+OPTIONS:   TeX:t LaTeX:t skip:nil d:nil todo:t pri:nil tags:not-in-toc
#+INFOJS_OPT: view:nil toc:nil ltoc:t mouse:underline buttons:0 path:http://orgmode.org/org-info.js
#+EXPORT_SELECT_TAGS: export
#+EXPORT_EXCLUDE_TAGS: noexport
#+LINK_UP:   
#+LINK_HOME: 
#+XSLT: 

#+startup: beamer
#+LaTeX_CLASS: beamer
#+LaTeX_CLASS_OPTIONS: [bigger,t]

#+BEAMER_FRAME_LEVEL: 2

#+latex_header: \definecolor{verylightgray}{rgb}{0.93,0.93,1.0}
#+latex_header: \mode<beamer>{\usetheme{progressbar}}
#+latex_header: \mode<handout>{\usecolortheme[rgb={0.5,0.5,0.5}]{structure}\usetheme[secheader]{Boadilla}\usepackage{pgfpages}\pgfpagesuselayout{4 on 1}[a4paper,landscape,border shrink=5mm]}
#+latex_header: \usepackage[absolute,overlay]{textpos}\setlength{\TPHorizModule}{1mm}\setlength{\TPVertModule}{1mm}\newcommand{\UCL}{\begin{textblock}{14}(120.0,0.0)\pgfuseimage{ucllogo}\end{textblock}}
#+ latex_header: \AtBeginSection[]{\begin{frame}<beamer>\frametitle{Topic}\tableofcontents[currentsection]\end{frame}}

#+latex_header: \usepackage{algorithm}
#+latex_header: \usepackage{algorithmic} %[noend] option possible
#+latex_header: \renewcommand{\algorithmicrequire}{\textbf{Given:}}
#+latex_header: \renewcommand{\algorithmicensure}{\textbf{Outputs:}}
#+latex_header: \usepackage{alltt}
#+latex_header: \usepackage{cancel}

#+ ------------------------ COMMANDS -------------------------
#+latex_header: \newcommand{\D}{{\mbox{d}}}
#+latex_header: \newcommand{\Diff}[2]{\frac{\D }{\D #2}#1}
#+latex_header: \newcommand{\diff}[2]{\frac{\D #1}{\D #2}}
#+latex_header: \newcommand{\HS}{\hspace*{1cm}}

#+latex_header: \date{$Revision: 1.7 $}\renewcommand{\date}[1]{}

#+ ------------------------ LISTINGS -------------------------
#+latex_header: \lstset{keywordstyle=\color{blue},commentstyle=\color{black!50!white},identifierstyle=\color{red!60!black}}

#+COLUMNS: %20ITEM %13BEAMER_env(Env) %6BEAMER_envargs(Args) %4BEAMER_col(Col) %7BEAMER_extra(Extra)

* Octave

*** Newton's method
***** The code						      :BMCOL:B_block:
      :PROPERTIES:
      :BEAMER_col: 0.5
      :BEAMER_env: block
      :END:
#+source: newtons-method
#+begin_src octave :exports both :results output
f = @(x) x^2 - 2;
df = @(x) 2*x;
x = 2 % initial guess
y = f(x)
while abs(y)>1e-5
  dy = df(x);
  x = x - y/dy
  y = f(x)
end
#+end_src
***** The output					      :BMCOL:B_block:
      :PROPERTIES:
      :BEAMER_col: 0.5
      :BEAMER_env: block
      :BEAMER_envargs: <2->
      :END:
#+results: newtons-method
: x =  2
: y =  2
: x =  1.5000
: y =  0.25000
: x =  1.4167
: y =  0.0069444
: x =  1.4142
: y =  6.0073e-06