File:Runge phenomenon equidist chebushev.gif
Summary
| Description |
Українська: Порівняння зміни помилки зі зростанням кількості вузлів інтерполяції функції Рунге використовуючи рівновіддалені вузли і вузли Чебишова |
| Date | |
| Source | Own work |
| Author | Igor Yalovecky |
| GIF development |
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
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import matplotlib.pyplot as plt
import numpy as np
import matplotlib.ticker as tckr
from matplotlib.animation import FuncAnimation
N=20
fig, (ax1, ax2) = plt.subplots(1,2)
fig.set_tight_layout(True)
def handle_nodes(x, order, ax, prefix):
y = lambda x : 1/(1+25*x*x);
p = np.poly1d(np.polyfit(x,y(x),order))
xd = np.linspace(-1,1,1000)
ax.cla()
ax.set_ylim(-5,5)
ax.set_title(prefix + ', порядок = ' + str(order))
ax.plot(xd,p(xd))
ax.plot(xd,y(xd))
(markerLines) = ax.stem(x,y(x),linefmt=' ',basefmt=' ',markerfmt='ro')
plt.setp(markerLines, markersize = 3)
def update(order):
if order >=2:
x = np.linspace(-1,1,order+1)
handle_nodes(x, order, ax1, 'рівновіддалені')
x = np.cos((2*np.arange(order+1)-1)*np.pi/(2*(order)))
handle_nodes(x, order, ax2, 'Чебишова')
else:
ax1.set_title('рівновіддалені вузли')
ax2.set_title('вузли Чебишова')
anim = FuncAnimation(fig, update, frames=np.arange(-10, N), interval=1000)
plt.show()