Analysis mit dem Computer by Alexandra Otto (auth.)

By Alexandra Otto (auth.)

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J- - h. - h J-k+l j (b. J,k-l - b. J-l,k-l ). (stelle [j-k+l] - stelle [j]) END PROC rekursion; (1.

REAL VAR X; get (x); REAL VAR wert :: koeff [1]; FOR i FROM 2 UPTO n REPEAT wert := wert * x + koeff [i] END REPEAT; put ("Der Wert an der Stelle x ="); put (x); put ("ist"); put (wert); line. ") ; get (antwort); IF antwort = "j" THEN berechne den wert ELSE LEAVE berechne funktionswerte Fr END REPEAT. In dem Programm werden mit Hilfe der Prozedur 'lagrange' zuerst der Reihe nach die Zähler der Lagrange - Polynome Li berechnet und diese dann durch den Wert des Zählerpolynoms an der betreffenden Nullstelle Xi dividiert, damit der Wert des Lagrange - Polynoms Li an der Stelle Xi auf 1 normiert ist.

Steigung 2. Steigung 3. Steigung 1 0 2 2/3 1 2 3 8 5 und damit das IllterpolatioIlspolynom p(x) 2 3 =3 x + 3I x + 2. Wollen wir explizit im Programm das Interpolationspolynom bestimmen, so müssen wir wie bei der Berechnung der Lagrang~ - Polynome die Koeffizienten der Produkte der Linearfaktoren bestimmen. Benötigen wir nur den Wert des Interpolationspolynoms an einer Stelle x, so können wir die Berechnung analog zum Horner - Schema durchführen. Gesucht ist für unser 2. 5. 5) 19 = "4' Programm zur Bestimmung des Interpoaltionspolynoms mit Hilfe der Newtonschen Interpolationsformel - in ELAN: REAL PROe steigung (INT eONST i, j): (schema [i][j-l] - schema [i-l][j-l])/ (stelle [i] - stelle [i-j+l] ) END PR oe steigung; deklariere die notwendigen variablen; hole stuetzpunkte; fOR zeile fROM 2 UPTO n REPEAT fOR spalte fROM 2 UPTO zeile REPEAT schema [zeile][spalte] := steigung (zeile,spalte); put (schema [zeile][spalte]); END REPEAT; line; END REPEAT; gib koeffizienten aus; frage nach neuen stuetzpunkten.

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