Beispiel: Rationale Funktionsregression 2

Funktionen > Datenanalyse > Kurvenanpassung > Beispiel: Rationale Funktionsregression 2

rationalfitnp - Keine Polstellen

Führen Sie mithilfe der Funktionen rationalfit und rationalfitnp eine rationale Funktionsregression durch. Wenn Sie die Funktion rationalfitnp statt der Funktion rationalfit verwenden, wird die Lösung des traditionellen Kleinste-Quadrate-Problems im Anpassungsintervall auf Wurzeln des Nenners geprüft. Wenn keine Polstellen vorhanden sind, wird die erzeugte Anpassung zurückgegeben. Sind Polstellen vorhanden, werden dem nichtlinearen Optimierungsproblem zusätzliche Nebenbedingungen hinzugefügt.

1. Definieren Sie einen Datensatz, indem Sie die inverse Funktion von x leicht abändern.

2. Geben Sie einen Grad für den Zähler und den Nenner der rationalen Funktion an.

Die Anpassungsfunktion hat folgende Form:

3. Definieren Sie eine Vertrauensgrenze und einen Vektor von Standardabweichungen.

4. Rufen Sie die Funktionen rationalfit und rationalfitnp auf.

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Für param1 und param2 gilt, dass die erste Spalte die Parameter enthält und die restlichen Spalten die unteren und oberen Schranken der einzelnen Parameter bei der oben definierten Vertrauensgrenze enthalten.

5. Stellen Sie den Datensatz und die beiden Regressionskurven grafisch dar.

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Die Polstelle wurde von der Funktion rationalfitnp entfernt. Das zugehörige Nennerpolynom wird in der folgenden Form dargestellt:

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Um die Polstelle zu vermeiden, wurden die folgenden Nebenbedingungen hinzugefügt:

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LeastSquaresFit

Vergleichen Sie die Anpassungskurven, die von rationalfitnp und LeastSquaresFit zurückgegeben werden. Die Funktion LeastSquaresFit verwendet denselben Algorithmus wie rationalfitnp, erfordert jedoch Schätzwerte und Vertrauensgrenzen für die Parameter. Sie sollten so vorgehen, wenn der Zähler statt der Nenner den konstanten Ausdruck enthalten soll.

1. Definieren Sie die Anpassungsfunktion.

2. Definieren Sie die Schätzwerte für die Parameter.

3. Definieren Sie untere und obere Randbedingungen für die Parameter.

4. Rufen Sie die Funktion LeastSquaresFit auf.

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5. Stellen Sie den Datensatz und die Anpassungskurven grafisch dar, die von den Funktionen rationalfitnp und LeastSquaresFit zurückgegeben werden.

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Jede Filter- oder Datentransformationsmethode, die die Daten gegen eine Gerade verschiebt, bevor eine rationale Funktionsregression durchgeführt wird, erhöht die Konvergenzgeschwindigkeit der Funktion rational beträchtlich und kann den zusätzlichen Vorteil haben, dass unerwünschte Polstellen wegfallen.

Zugehörige Themen

Rationale Funktionsregression

LeastSquaresFit und Vertrauensfunktionen

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