318 Kapitel 10. Differentialrechnung für Funktionen mehrerer Veränderlicher
0,2-
Abb. 10.17: Umsatzmaximum
bei konkurrierenden Produkten
Messwerte die Funktionsgleichung (10.45) exakt erfüllen. Die Aufgabe besteht vielmehr
darin, die unbekannten Parameter an die Daten möglichst gut anzupassen.
• Extremalaufgabe für eine Funktion von k + 1 Variablen:
η
F(a) = F(a
0
,..., a
k
) = ^ (/(x»; o
0
,..., a
k
) - y¿)
2
->· Min. (10.46)
i=l
Die hierin auftretende Fehlersumme setzt sich aus den Quadraten der Differenzen zwischen
den einzelnen Messwerten y, und den Funktionswerten }(x
t
\...) mit den zu bestimmenden
Parametern zusammen. Daher rührt die auf Gauβ zurückgehend ...
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