Folien CE, FoC

ws2011/CE/Uebungen/3. Programmieraufgabe/Vorlage_P3/fixpoint.m

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+function [N,X_itn] = fixpoint (x)
+
+% Function fixpoint with relaxation matrix
+% In: Start value
+% Out: number of iteration steps, vector of solution
+
+% Todo: Replace below code with fixpoint method
+N=1;
+X_itn=x;
+
+

ws2011/CE/Uebungen/3. Programmieraufgabe/Vorlage_P3/main.m

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+function main();
+
+% Main function for iteration of static values in 
+% pendulum with newton and fixed point method. 
+%
+%
+% Grundlagen der Modellierung und Simulation
+% SoSe 2011
+
+
+%%%%%%%%%%%%%%%%%%%%%% Start Values %%%%%%%%%%%%%%%%%%%%
+
+x = [10; 0];
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+x_newton = x;
+x_fixpunkt = x;
+x_qnewton = x;
+
+%%%%%%%%%%%%%%%%%%% Newton %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+[it_n, x_n] = newton(x_newton);
+
+%%%%%%%%%%%%%%%%%%% Fixpunkt %%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+[it_f, x_f] = fixpoint(x_fixpunkt);
+
+%%%%%%%%%%%%%%%%%%% Quasi-Newton %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+[it_qn, x_qn] = quasi_newton(x_qnewton);
+
+
+%%%%%%%%%%%%%%%%%%% Output %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+disp('Startwert x');
+[x(1), x(2)]
+disp('Anzahl Iterationen bei Newton:');
+it_n
+disp('Loesung:');
+x_n(1,it_n)
+disp('Anzahl Iterationen bei Fixpunkt:');
+it_f
+disp('Loesung:');
+x_f(1,it_f)
+disp('Anzahl Iterationen bei Quasi-Newton:');
+it_qn
+disp('Loesung:');
+x_qn(1,it_qn)
+
+it_ges = max(it_n,max( it_f,it_qn));
+
+for i = 1:it_ges
+  anzahl_ges(i) = i;
+end
+
+
+if(it_n < it_ges)
+  for i = it_n+1:it_ges
+    x_n(1,i) = x_n(1,i-1);
+    x_n(2,i) = x_n(2,i-1);
+  end
+end
+
+if(it_f < it_ges)
+  for i = it_f+1:it_ges
+    x_f(1,i) = x_f(1,i-1);
+    x_f(2,i) = x_f(2,i-1);
+  end
+end
+if(it_qn < it_ges)
+  for i = it_qn+1:it_ges
+    x_qn(1,i) = x_qn(1,i-1);
+    x_qn(2,i) = x_qn(2,i-1);
+  end
+end
+
+
+plot(anzahl_ges, x_n(1,:), ... 
+     anzahl_ges, x_f(1,:), ...
+     anzahl_ges, x_qn(1,:), ... 
+     anzahl_ges, x_n(2,:), ...
+     anzahl_ges, x_f(2,:),...
+     anzahl_ges, x_qn(2,:)); 
+title('Iterationsverfahren');
+legend('Theta (Newton) ','Theta (FixP)','Theta (Quasi-Newton)','Theta-Punkt (New.)','Theta-Punkt(Fixp)','Theta-Punkt(Quasi-New.)' )
+xlabel('Anzahl Iterationen');
+ylabel('Iterationsergebnisse');
+

ws2011/CE/Uebungen/3. Programmieraufgabe/Vorlage_P3/matrikelnummer.m

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+%-----------------------------------------------------------------
+% Die nachfolgende Funktion liefert als Rückgabewert die Matrikelnummer
+% und den Namen des/der abgebenden Studenten/Studentin.
+%-----------------------------------------------------------------
+function [m, n, g] = matrikelnummer()
+% Bitte tragen Sie hier Ihre Matrikelnummer ein:
+m = 1234567;
+% Bitte tragen Sie hier Ihren Namen ein:
+n = 'Max Mustermann';
+% Bitte tragen Sie hier zusätzlich die Matrikelnummern der Gruppen-
+% mitglieder ein, mit denen Sie zusammengearbeitet haben oder lassen Sie
+% die Variable unverändert:
+g = [m,0,0];
+end

ws2011/CE/Uebungen/3. Programmieraufgabe/Vorlage_P3/newton.m

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+function [N,X_itn] = newton(x);
+
+% Function newton
+% In: Start value
+% Out: number of iteration steps, vector of solution
+
+% Todo: Replace below code with newton method
+N=1;
+X_itn=x;
+

ws2011/CE/Uebungen/3. Programmieraufgabe/Vorlage_P3/quasi_newton.m

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+function [N,X_itn] = quasi_newton(x);
+
+% Function quasi_newton
+% In: Start value
+% Out: number of iteration steps, vector of solution
+
+% Todo: Replace below code with quasi newton method
+N=1;
+X_itn=x;