Functions and Analysis

    

Why Quasi-Interpolation onto Manifold has Order 4

Authors: M. Sprecher

We consider approximations of functions from samples where the functions take values on a submanifold of $\mathbb{R}^n$. We generalize a common quasi-interpolation scheme based on cardinal B-splines by combining it with a projection $P$ onto the manifold. We show that for $m\geq 3$ we will have approximation order $4$. We also show why higher approximation order can not be expected when the control points are constructed as projections of the filtered samples using a fixed mask.

Comments: 7 Pages. typos corrected and reference added

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Submission history

[v1] 2020-04-12 04:40:45
[v2] 2020-04-13 03:07:17

Unique-IP document downloads: 313 times

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