By Alexandra Otto (auth.)

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**Additional info for Analysis mit dem Computer, 1st Edition**

**Example text**

1, •.. 9). Wir wenden das Dreiecksschema auf unser zweites Beispiel an. Stützpunkte sind (-1;1), (0;2), (1;3) 1. Steigung 1 o 2 o 3 p(x) =x 2 + ist die Gerade durch die drei gegebenen Punkte. 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.

Programm zur Interpolation mit dem Lagrange - Verfahren -in ELAN: PROC lagrange (INT CONST i): uebertrage die stuetzstellen; erstelle das schema; normiere das polynom; notiere die koeffizienten. - stuetzstellen [zeile+l] FI END REPEAT. erstelle das schema: ROW 9 ROW 9 REAL VAR schema; schreibe die erste zeile; FOR zeile FROM 2 UPTO n-l REPEAT berechne das erste element der zeile; berechne weitere elemente der zeile END REPEAT. schreibe die erste zeile: schema [1][1] := - stellen [11. perechne das erste element der zeile: schema [zeile][l] := schema [ieile-l][l] - stellen [zeile1.

Die Rekursionsformel lautet h. b. J,k b. 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.