Merge remote-tracking branch 'upstream/master'

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diff --git a/buch/chapters/40-eigenwerte/images/wa.m b/buch/chapters/40-eigenwerte/images/wa.m
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+++ b/buch/chapters/40-eigenwerte/images/wa.m
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+#
+# wa.m -- Wurzelapproximation
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+global u;
+global N;
+global t;
+global s;
+
+N = 100;
+n = 10;
+s = 1;
+
+u = zeros(N + 2, n);
+t = (0:N+1)' / N;
+t = t.^2;
+
+for i = (2:n)
+	u(:,i) = u(:,i-1) + 0.5 * (t-u(:,i-1).^2);
+end
+
+u
+
+global f;
+f = fopen("wa.tex", "w");
+fprintf(f, "%%\n");
+fprintf(f, "%% Approximation der Wurzelfunktion\n");
+fprintf(f, "%%\n");
+
+function pfad(i, name)
+	global f;
+	global u;
+	global t;
+	global N;
+	fprintf(f, "\\def\\pfad%s{\n", name);
+	fprintf(f, "(%.4f,%.4f)\n", t(1,1), u(1,i));
+	for j = (2:N+1)
+		fprintf(f, "--(%.4f,%.4f)\n", t(j,1), u(j,i));
+	end
+	fprintf(f, "}\n");
+end
+
+pfad( 1, "a")
+pfad( 2, "b")
+pfad( 3, "c")
+pfad( 4, "d")
+pfad( 5, "e")
+pfad( 6, "f")
+pfad( 7, "g")
+pfad( 8, "h")
+pfad( 9, "i")
+pfad(10, "j")
+
+function fehler(i, name)
+	global f;
+	global u;
+	global t;
+	global N;
+	global s;
+	fprintf(f, "\\def\\fehler%s{\n", name);
+	fprintf(f, "(%.4f,%.4f)\n", t(1,1), s*(sqrt(t(1,1))-u(1,i)));
+	for j = (2:N+2)
+		fprintf(f, "--(%.4f,%.4f)\n", t(j,1), s*(sqrt(t(j,1))-u(j,i)));
+	end
+	fprintf(f, "}\n");
+end
+
+fehler( 1, "a")
+fehler( 2, "b")
+fehler( 3, "c")
+fehler( 4, "d")
+fehler( 5, "e")
+fehler( 6, "f")
+fehler( 7, "g")
+fehler( 8, "h")
+fehler( 9, "i")
+fehler(10, "j")
+
+fclose(f);