Esempio: interpolazione polinomiale

Funzioni > Analisi dati > Interpolazione e predizione > Esempio: interpolazione polinomiale

polyint

Utilizzare la funzione polyint per eseguire l'interpolazione polinomiale in un insieme di dati.

1. Definire un insieme di dati.

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2. Chiamare la funzione polyint per calcolare l'interpolazione polinomiale dell'insieme di dati in corrispondenza di un punto particolare.

In corrispondenza di x = 328, il risultato interpolato è y = -0.189, con un errore di 0,056.

3. Definire l'intervallo di valori x in cui si desidera trovare i valori y interpolati.

4. Registrare i valori interpolati e il rispettivo errore.

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5. Tracciare il grafico dei punti dati, della curva interpolata e della stima di errore.

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polycoeff

Per calcolare i valori interpolati, utilizzare polyint. Per calcolare sia il polinomio di interpolazione che alcune delle sue derivate, utilizzare polycoeff. I coefficienti forniti da polycoeff sono meno accurati in corrispondenza di punti dati specifici, pertanto non costituiscono la rappresentazione migliore dei valori interpolati.

1. Trovare i coefficienti di un polinomio per la curva polinomiale che passa per l'insieme di punti dati definito in precedenza.

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2. Definire una funzione polinomiale, dove c è il vettore di coefficienti di un polinomio.

3. Differenziare la funzione polinomiale.

4. Tracciare il grafico dei punti dati, dell'interpolazione polinomiale e della derivata prima.

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La funzione polycoeff non costruisce il polinomio del best fit ai minimi quadrati, in quanto questa operazione viene eseguita dalla funzione polyfit.

I risultati di polyint e polycoeff non devono essere utilizzati per effettuare predizioni per i valori y esterni all'intervallo dei valori x originali.

polyiter

Utilizzare la funzione polyiter per eseguire un'interpolazione polinomiale.

1. Definire il numero massimo possibile di iterazioni e la tolleranza.

2. Chiamare la funzione polyiter.

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L'algoritmo non converge e pertanto non si arresta prima dell'iterazione N_max. Non viene ottenuto un errore di 0,01 e viene restituito lo stesso risultato di polyint:

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3. Tracciare il grafico dei punti originali, del polinomio esatto e del polinomio iterato.

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