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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);
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