Size of this PNG preview of this SVG file: 450 × 360 pixels. Other resolutions: 300 × 240 pixels | 600 × 480 pixels | 960 × 768 pixels | 1,280 × 1,024 pixels | 2,560 × 2,048 pixels.
Original file (SVG file, nominally 450 × 360 pixels, file size: 33 KB)
 | This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. |
Summary
| Description |
English: For the Fast Multipole Method in 1D, this illustrates the interpolation of a pole at x=3 with an order-5 Chebyshev polynomial around [-1, 1] |
| Date | |
| Source | Own work |
| Author | Summentier |
Generated from the following Python script:
import numpy as np
import numpy.polynomial.chebyshev as np_cheby
import matplotlib.pyplot as pl
def f(x):
x = np.asarray(x)
with np.errstate(divide='ignore'):
return 1 / (x - 3)
ftilde = np_cheby.Chebyshev.interpolate(f, 5)
tk, _ = np_cheby.chebgauss(5)
pl.figure(figsize=(5,4))
x = np.linspace(-2, 4, 121)
xint = np.linspace(-1, 1, 101)
pl.plot(x, f(x), '-r', label='$(y-3)^{-1}$')
pl.plot([3,3], [-10,10], ':r', lw=1)
pl.plot(xint, ftilde(xint), '-k', label=r'$P_5(y)$')
pl.plot(x, ftilde(x), '--k', lw=1.2)
pl.plot(tk, ftilde(tk), '+k', lw=1, label='Chebyshev nodes')
pl.legend()
pl.ylim(-5, 5)
pl.xlim(-1.5, 4)
pl.title(r"Local expansion of a pole at $x=3$")
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 13:30, 9 November 2023 | | 450 × 360 (33 KB) | Summentier | Uploaded own work with UploadWizard |
File usage
The following page uses this file:
Global file usage
The following other wikis use this file:
- Usage on ca.wikipedia.org
