add more stuff about spectral radius

4 files changed, 126 insertions, 0 deletions

diff --git a/buch/chapters/40-eigenwerte/images/Makefile b/buch/chapters/40-eigenwerte/images/Makefile
new file mode 100644
index 0000000..5915d30
--- /dev/null
+++ b/buch/chapters/40-eigenwerte/images/Makefile
@@ -0,0 +1,13 @@
+#
+# Makefile
+#
+# (c) 2020 Prof Dr Andreas Müller, Hochschule Rappersil
+#
+all:	sp.pdf 
+
+sp.pdf:	sp.tex sppaths.tex
+	pdflatex sp.tex
+
+sppaths.tex:	spbeispiel.m
+	octave spbeispiel.m
+
diff --git a/buch/chapters/40-eigenwerte/images/sp.pdf b/buch/chapters/40-eigenwerte/images/sp.pdf
new file mode 100644
index 0000000..5346e06
--- /dev/null
+++ b/buch/chapters/40-eigenwerte/images/sp.pdf
diff --git a/buch/chapters/40-eigenwerte/images/sp.tex b/buch/chapters/40-eigenwerte/images/sp.tex
new file mode 100644
index 0000000..db70889
--- /dev/null
+++ b/buch/chapters/40-eigenwerte/images/sp.tex
@@ -0,0 +1,62 @@
+%
+% sp.tex -- template for standalon tikz images
+%
+% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{2.33}
+\input{sppaths.tex}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\xdef\sx{1}
+\xdef\sy{1}
+
+% add image content here
+\begin{scope}
+\begin{scope}
+\clip (0,0) rectangle (3,2.1);
+\richardson
+\end{scope}
+\draw[->] (-0.1,0) -- (3.15,0) coordinate[label={$\tau$}];
+\draw[->] (0,-0.1) -- (0,2.3) coordinate[label={right:$\varrho(\frac1\tau A-E)$}];
+\draw (1,{-0.1/\skala}) -- (1,{0.1/\skala});
+\draw (2,{-0.1/\skala}) -- (2,{0.1/\skala});
+\draw (3,{-0.1/\skala}) -- (3,{0.1/\skala});
+\node at (1,{-0.1/\skala}) [below] {1};
+\node at (2,{-0.1/\skala}) [below] {2};
+\node at (3,{-0.1/\skala}) [below] {3};
+\draw ({-0.1/\skala},1) -- ({0.1/\skala},1);
+\draw ({-0.1/\skala},2) -- ({0.1/\skala},2);
+\node at ({-0.1/\skala},1) [left] {1};
+\node at ({-0.1/\skala},2) [left] {2};
+\end{scope}
+
+\xdef\sy{1}
+
+\begin{scope}[xshift=3.5cm]
+\begin{scope}
+\clip (0,0) rectangle (2,2);
+\sor
+\end{scope}
+\draw[->] (-0.1,0) -- (2.15,0) coordinate[label={$\omega$}];
+\draw[->] (0,-0.1) -- (0,2.3) coordinate[label={right:$\varrho(B_\omega^{-1}C_\omega)$}];
+\draw (1,{-0.1/\skala}) -- (1,{0.1/\skala});
+\draw (2,{-0.1/\skala}) -- (2,{0.1/\skala});
+\node at (1,{-0.1/\skala}) [below] {1};
+\node at (2,{-0.1/\skala}) [below] {2};
+\draw ({-0.1/\skala},1) -- ({0.1/\skala},1);
+\draw ({-0.1/\skala},2) -- ({0.1/\skala},2);
+\node at ({-0.1/\skala},1) [left] {1};
+\node at ({-0.1/\skala},2) [left] {2};
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/40-eigenwerte/images/spbeispiel.m b/buch/chapters/40-eigenwerte/images/spbeispiel.m
new file mode 100644
index 0000000..81160b9
--- /dev/null
+++ b/buch/chapters/40-eigenwerte/images/spbeispiel.m
@@ -0,0 +1,51 @@
+#
+# spbeispiel.m
+#
+# (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil
+#
+N = 30
+R = 0.05 * rand(N,N);
+R = R + R';
+A = eye(N) + R;
+L = tril(A,-1)
+U = tril(A',-1)'
+D = diag(diag(A))
+
+A
+
+function r = spektralradius(A)
+	r = max(abs(eig(A)));
+end
+
+gaussseidel = spektralradius(inverse(L+D)*U)
+jacobi = spektralradius(inverse(D)*(L+U))
+richardson = spektralradius(A - eye(N))
+
+fd = fopen("sppaths.tex", "w");
+
+fprintf(fd, "\\def\\richardson{\n")
+tau = 0.1;
+r = spektralradius((1/tau) * A - eye(N))
+fprintf(fd, "\\draw[line width=1.4pt,color=red] ({\\sx*0.1},{\\sy*%.5f})", r);
+for tau = (11:300) / 100
+	r = spektralradius((1/tau) * A - eye(N));
+	fprintf(fd, "\n--({\\sx*%.5f},{\\sy*%.5f})", tau, r);
+end
+fprintf(fd, "\n;}\n");
+
+fprintf(fd, "\\def\\sor{\n");
+omega = 1/100
+B = (1/omega) * D + L;
+C = (1-1/omega) * D + U;
+r = spektralradius(inverse(B) * C)
+fprintf(fd, "\\draw[line width=1.4pt,color=red] ({\\sx*%.3f},{\\sy*%.3f})", omega, r);
+for omega = (2:200) / 100
+	B = (1/omega) * D + L;
+	C = (1-1/omega) * D + U;
+	r = spektralradius(inverse(B) * C);
+	fprintf(fd, "\n--({\\sx*%.5f},{\\sy*%.5f})", omega, r);
+end
+fprintf(fd, ";\n}\n");
+
+fclose(fd);
+