File:Runge phenomenon.svg
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Summary
| Description |
English: The red curve is the Runge function.
The blue curve is a 5th-order interpolating polynomial (using six equally spaced interpolating points). The green curve is a 9th-order interpolating polynomial (using ten equally spaced interpolating points). At the interpolating points, the error between the function and the interpolating polynomial is (by definition) zero. Between the interpolating points (especially in the region close to the endpoints 1 and −1), the error between the function and the interpolating polynomial gets worse for higher-order polynomials.Español: La curva roja es la función de Runge.
La curva azul es un polinomio interpolante de orden 5 (usando seis puntos equiespaciados). La curva verde es un polinomio interpolante de orden 9 (usando diez puntos equiespaciados). A los puntos interpolantes el error entre la función y el polinomio interpolantes es cero (por definición). Entre estos puntos (especialmente cerca de los extremos 1 y -1) el error entre la función y el polinomio interpolante incrementa conforme el polinomio aumenta de orden. |
| Date | |
| Source | Own work |
| Author | Nicoguaro |
| SVG development | |
| Source code | Python codefrom __future__ import division
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import lagrange
from matplotlib import rcParams
rcParams['font.family'] = 'serif'
rcParams['font.size'] = 16
def runge(x):
return 1/(1 + 25*x**2)
plt.figure(figsize=(8,8))
npts = 201
# Runge Function
x_vec = np.linspace(-1, 1, npts)
y_vec = runge(x_vec)
plt.plot(x_vec, y_vec, lw=2, color='r')
# Fifth degree polynomial
pts_x = np.linspace(-1, 1, 6)
pts_y = runge(pts_x)
poly = lagrange(pts_x, pts_y)
y_interp = poly(x_vec)
plt.plot(x_vec, y_interp, lw=2, color='b')
# Ninth degree polynomial
pts_x = np.linspace(-1, 1, 10)
pts_y = runge(pts_x)
poly = lagrange(pts_x, pts_y)
y_interp = poly(x_vec)
plt.plot(x_vec, y_interp, lw=2, color='g')
plt.savefig("Runge_phenomenon.svg")
plt.show()
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 00:40, 23 October 2015 | | 720 × 720 (24 KB) | wikimediacommons>Nicoguaro | User created page with UploadWizard |
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