Berechnung der Quadratwurzel
Bearbeitungszeit: ca. 10 Minuten für erste Lösung; ca. 15 Minuten für beide Lösungen.
Implementieren Sie eine Methode sqrt ( double x , double epsilon ) , die die Quadratwurzel von x mit einer Genauigkeit von epsilon berechnet. Verwenden Sie dazu das Newton-Raphson-Verfahren: \(y_{n+1} = \frac{1}{2}\left(y_n + \frac{x}{y_n}\right)\) . Implementieren Sie die Methode einmal rekursiv und einmal iterativ.
Der Abbruch soll erfolgen, wenn \(|y_{n+1} - y_n| < \epsilon\) .
Hinweis
Für die rekursive Variante kann es sinnvoll sein neben der Hauptmethode eine zweite Hilfsmethode zu implementieren.
Beispiel
Enter number to compute SQRT for : 9
Enter epsilon: 0 .0001
9 .0 = > 5 .0
...
3 .00009155413138 = > 3 .000000001396984
The SQRT of 9 .0 is 3 .000000001396984
MTAwMDAw:Epcs+HLsu4MUxLmf3Tk8jVXKMX6NzGH+X7VokjOc7h8=:oMKfNFmK+mPQTygr: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