File:Rho-Lagrange.svg
Jump to navigation
Jump to search
Size of this PNG preview of this SVG file: 800 × 479 pixels. Other resolutions: 320 × 192 pixels | 640 × 383 pixels | 1,024 × 613 pixels | 1,280 × 767 pixels | 2,560 × 1,533 pixels | 1,152 × 690 pixels.
Original file (SVG file, nominally 1,152 × 690 pixels, file size: 2 KB)
Summary
| Description |
English: In cubic Lagrange interpolation, optimal node t and critical point xc are related through xc + t = √ρ, with plastic ratio ρ the real root of x3 = x + 1, t = √ρ/(ρ2 + 1) and xc = ρ2t. The constants can be expressed as geometric series, in which the terms correspond to diagonal lengths of rectangles with edges in ratio ρ2. The diagram shows the sequences for xc (red) and t (green) converge at a single point on the diagonal of a rho-squared rectangle with length √ρ. |
| Date | |
| Source | Own work |
| Author | Zilverspreeuw |
| SVG development |
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 | 17:24, 10 January 2025 | | 1,152 × 690 (2 KB) | wikimediacommons>Zilverspreeuw | Positioning |
File usage
The following page uses this file:
