File:Rho-Lagrange.svg
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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 |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 16:24, 10 January 2025 | | 1,152 × 690 (2 KB) | wikimediacommons>Zilverspreeuw | Positioning |
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