Esempio: interpolazione di Thiele

Funzioni > Analisi dati > Interpolazione e predizione > Esempio: interpolazione di Thiele

Eseguire l'interpolazione a frazione continua di Thiele in un insieme di dati.

Thielecoeff e Thiele

Utilizzare le funzioni Thielecoeff e Thiele per interpolare un insieme di dati restituito da una funzione razionale.

1. Definire il numero di punti di interpolazione.

2. Definire una funzione razionale, ad esempio la funzione Lorentzian.

3. Prendere in considerazione campioni della funzione e registrarne i valori x e y nei vettori.

4. Utilizzare la funzione Thielecoeff per trovare i coefficienti della frazione continua appropriata per i punti campionati.

5. Chiamare la funzione Thiele per eseguire l'interpolazione.

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Le funzioni Thiele vengono eseguite correttamente, mentre per la funzione rationalint si verificano errori in alcuni punti dell'intervallo di interpolazione. Tali errori sono dovuti al fatto che i dati sono simmetrici e causano errori di divisione per zero in corrispondenza di alcuni valori di x intermedi.

6. Tracciare il grafico della funzione originale, dei punti campionati e della curva interpolata.

Fare clic per copiare questa espressione

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7. Tracciare il grafico in cui sono indicati i residui dell'interpolazione di Thiele.

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Ordine dei punti

Se a due punti adiacenti sono assegnati valori di y identici, l'algoritmo non restituirà i valori corretti. Per ottenere il risultato corretto, è necessario riordinare i dati.

1. Definire un insieme di punti.

2. Trovare i coefficienti della funzione Thiele.

I coefficienti sono troppo grandi.

3. Riordinare i dati per ottenere una soluzione appropriata.

4. Ripetere l'operazione descritta al passo 2.

5. Definire la funzione interpolata.

6. Tracciare il grafico della funzione interpolata e dei punti dati originali.

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