updated&new ue.pdf, spicker started

texnotes/num2Notes.tex

@@ -129,9 +129,7 @@
 \begin{document}
 	\pagestyle{fancy}
 
-%	\include{ue1}
-%	\include{ue2}
-	\include{ue3}
+	\input{spicker01}
 
 \end{document}
 

texnotes/num2Spicker.tex

@@ -0,0 +1,193 @@
+\documentclass[12pt]{article}
+
+\usepackage{amsmath,amssymb, a4, verbatim}
+\usepackage[german]{babel}
+%\usepackage[latin1]{inputenc}
+\usepackage[utf8]{inputenc} % üöäß
+\usepackage{listings} % für inline codelistings
+\lstset{%
+	basicstyle=\ttfamily,	% the size of the fonts 
+	columns=fixed,			% anything else is horrifying
+	showspaces=false,	    % show spaces using underscores?
+	showstringspaces=false,	% underline spaces within strings?
+	showtabs=false,			% show tabs within strings?
+	xleftmargin=1.5em,		% left margin space
+}
+\lstdefinestyle{inline}{basicstyle=\ttfamily}
+\newcommand{\listline}[1]{\lstinline[style=inline]!#1!}
+
+
+\usepackage{caption}
+\newcommand{\tinycaption}[1]{\captionsetup{labelformat=empty}\caption{#1}}
+
+%\usepackage{color}
+%\usepackage{epsfig} % eps
+\usepackage{graphicx} % eps
+%\usepackage[shortcuts]{extdash}
+%\usepackage{dsfont}
+%\usepackage{epstopdf} % eps
+%\usepackage[pdf]{pstricks} % eps
+%\usepackage{auto-pst-pdf}
+\usepackage{mathtools}
+\usepackage{dsfont} % $ \mathds{1} $
+%\usepackage{icomma}
+\usepackage{tikz}
+%\usepackage{pgfplots}
+%\pgfplotsset{compat=1.8}
+\usepackage[bottom]{footmisc} % put footnotes at the bottom of page
+\usepackage{nicefrac} % für brüche die aussehen wie prozentzeichen
+% \usepackage{ps2pdf}
+\usetikzlibrary{automata,positioning}
+
+\usepackage{algorithmicx}
+\usepackage{algpseudocode}
+\usepackage{algorithm}
+
+\usepackage{multicol}
+\usepackage{wrapfig} % make stuff float
+\usepackage{placeins} % stop stuff from floating
+\usepackage{seqsplit} % very long numbers
+\usepackage{framed} % begin{framed}
+
+%  Headings and Footings :
+%\usepackage{fancyhdr}
+%\headheight15pt
+%\lhead{Numerik II, \ueberschrift}
+
+%\chead{}
+%\rhead{\thepage}
+%\renewcommand{\headrulewidth}{.4pt}
+
+%\lfoot{\today}
+%\cfoot{}
+%\rfoot{Joshua}
+%\renewcommand{\footrulewidth}{.4pt}
+
+%----------------------------------------------------------------
+
+%\textwidth16.5cm
+%\oddsidemargin0.cm
+%\evensidemargin0.cm
+
+\def\somedistanceLeft{10mm}%2cm}
+\def\somedistanceTop{10mm}%3cm}
+
+\usepackage{geometry}
+\geometry{
+	a4paper, % or A3, etc if to print smaller
+%	total={170mm,257mm},
+	left=\somedistanceLeft,
+	right=\somedistanceLeft,
+	top=\somedistanceTop,
+	bottom=\somedistanceTop,
+	landscape % better i think
+}
+
+
+\parindent0cm
+
+\usepackage{cancel}
+
+\newcommand{\R}{ {\mathbb R} }
+\newcommand{\C}{ {\mathbb C} }
+\newcommand{\1}{ {\mathds{1}} }
+\newcommand{\abs}[1]{\lvert#1\rvert}
+\newcommand{\norm}[1]{\left\lVert#1\right\rVert}
+\newcommand{\xt}{\tilde{x}}
+\newcommand{\dotleq}{\dot{\leq}}
+\newcommand{\m}{\hphantom{-} }
+
+\newcommand{\dashfill}[1]{\vspace{11pt}\def\dashfill{\cleaders\hbox{#1}\hfill}\hbox to \hsize{\dashfill\hfil}\vspace{11pt}}
+\newcommand{\scdot}{\!\cdot\!}
+
+
+\newcommand{\sig}{\text{signum}}
+\newcommand{\rot}{}
+
+% ------------------  edit Ueberschrift ---------------------
+\newcommand{\ueberschrift}{Numerik II Notizen}
+
+
+\usepackage{mathpazo}
+\usepackage[mathpazo]{flexisym}
+\usepackage{breqn}
+
+% https://tex.stackexchange.com/questions/110393/too-wide-figure-caption
+% ffs \usepackage{boxhandler}
+
+\newcommand{\scalprod}[2]{\left\langle\,#1\,;\,#2\,\right\rangle}
+
+\usepackage{url}
+
+\usepackage{pdfpages}
+%\usepackage{showframe}
+% -----------------------------------------------------------
+
+
+%\texttt{} num.num.alph as headings
+\renewcommand{\thesubsubsection}{\thesubsection.\alph{subsubsection}}
+
+\begin{document}
+	\pagestyle{empty} % no line numbers
+
+	% equation spacing
+	\def\distEQ{12pt}
+	\abovedisplayskip=\distEQ plus 0pt minus \distEQ
+	\abovedisplayshortskip=0pt plus 0pt
+	\belowdisplayskip=\distEQ plus 0pt minus \distEQ
+	\belowdisplayshortskip=7pt plus 0pt minus 7pt
+
+	% line between collumns
+	\setlength{\columnsep}{5mm}
+	\setlength{\columnseprule}{1pt}
+	\begin{multicols}{2}
+		\input{spicker01}
+	\end{multicols}
+
+\end{document}
+
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texnotes/spicker01.tex

@@ -0,0 +1,20 @@
+\begin{minipage}[tc]{\linewidth}
+	Lineares Ausgleichsproblem:
+	\begin{tabular}{cl}
+		\begin{tabular}{r|c|c|c|c}
+			$t_i$ & 0 & 1 & 2 & 3 \\ 
+			\hline 
+			$y_i$ & 3 & $2,14$ & 1,8 & 1,72 \\ 
+		\end{tabular}  & Daten \\ 
+		func & Modellfunktion \\ 
+	\end{tabular} 
+\end{minipage}
+
+\begin{minipage}[tc]{\linewidth}
+	Satz: 1.1: \linebreak[3]
+	$x^*\in \R$ ist genau dann eine Lösung des linearen Ausgleichsproblems, 
+	wenn $x^*$ Lösung der Normalgleichung $A^TAx = A^Tb$ ist.
+	Es gibt mindestens eine Lösung $x^*$.
+	Sie ist eindeutig, gdw. $Rang(A) = n$.
+\end{minipage}
+

uebungen/.gitignore

@@ -0,0 +1 @@
+*.asv

uebungen/factorio/funcApprox/logbApprox.m

@@ -8,6 +8,11 @@
 limit_end = 3e5;
 base = (limit_end)^(1/100); % of the log, meaning logb(limit_end) := 100 
 logb = @(x) log(x)/log(base);
+%ableitung
+logbA1 = @(x) 1 ./ (x .* log(base));
+logbA2 = @(x) - 1 ./ (x .^ 2 .* log(base));
+logbA3 = @(x) 2 ./ (x .^ 3 .* log(base));
+
 
 n = 10; % amount of nodes
 

uebungen/lagrangePolynom.m

@@ -0,0 +1,8 @@
+function [ y ] = lagrangePolynom( j, knoten, x )
+    y = ones(size(x));
+    for i = 1:length(knoten)
+        if j == i ; continue; end;
+        y = y .* (x-knoten(i)) ./ (knoten(j)-knoten(i));
+    end
+end % function
+

uebungen/ue5_3.m

@@ -0,0 +1,57 @@
+format compact;
+format shortg;
+clear all;
+close all;
+
+n = 6;
+nPoints = n*100;
+more = 0.02*0;
+x = linspace(-1-more,1+more,nPoints);
+
+funToInterp = @(t) sin(t*pi);
+
+
+%% lagrange
+subplot(2,1,1);
+hold on;
+
+xiEqual = -1 +2* (0:n) ./ n
+
+plot(xiEqual, 1, 'o', 'HandleVisibility','off');
+allY = zeros(size(x));
+for j=(0:n)+1
+    y = lagrangePolynom(j, xiEqual, x);
+    allY = allY + y*funToInterp(xiEqual(j));
+    plot(x,y, 'HandleVisibility','off');
+    axis tight;
+end
+plot(x, allY, '-g.', 'DisplayName', 'Approximation');
+err = abs(funToInterp(x)-allY);
+max(err)
+plot(x, err, '-r.', 'DisplayName', 'Error');
+plot(x, funToInterp(x), '-b', 'DisplayName', 'funToInterp');
+legend show;
+
+%% tschebyschow
+subplot(2,1,2);
+hold on;
+
+xiTsche = -cos((2*(0:n)+1) / (2*n + 2) * pi);
+
+plot(xiTsche, 1, 'o', 'HandleVisibility','off');
+allY = zeros(size(x));
+for j=(0:n)+1
+    y = lagrangePolynom(j, xiTsche, x);
+    allY = allY + y*funToInterp(xiTsche(j));
+    plot(x,y, 'HandleVisibility','off');
+    axis tight;
+end
+plot(x, allY, '-g.', 'DisplayName', 'Approximation');
+err = abs(funToInterp(x)-allY);
+max(err)
+plot(x, err, '-r.', 'DisplayName', 'Error');
+plot(x, funToInterp(x), '-b', 'DisplayName', 'funToInterp');
+
+legend show;
+
+