tudelft3d / terrainbook

"Computational modelling of terrains" book: source code + PDF
https://tudelft3d.github.io/terrainbook/
Creative Commons Attribution 4.0 International
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Fig 4.3 (b) showing Runge's effect #16

Closed pratyush1611 closed 3 years ago

pratyush1611 commented 3 years ago

The text says that Runge's Phenomenon is observed when the polynomial overshoots at samples. In the figure, the polynomial is supposed to be $C^2$ i.e. continuous and smooth so that it can be differentiated at all points, however, at around x=5, there is a sharp change in the polynomial curve, where it won't be differentiable and thus not $C^2$ (since the limit of a function doesn't exist at points where the slope changes abruptly)

hugoledoux commented 3 years ago

you're totally right, cheers. Fixed.