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# Questions tagged [interpolation]

Interpolation is the theory of constructing smooth functions, usually polynomials or trigonometric polynomials, whose graph passes through a number of given points in the plane. Splines and Bézier curves, piecewise linear or cubic interpolation, Lagrange and Hermite interpolation are example topics.

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### Thin-Plate-Spline understanding and solution

This is a migrated question from: Thin-Plate-Spline understanding and solution. If I need to delete one of the questions let me know. I was suggested to post it here as well. As I understand it a Thin-...
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### K functional of $L^{1,\infty}$ and $L^\infty$ real interpolation

I want to know where can I find how to compute, given a function $f$ and $t>0$ $$K(t,f;L^{1,\infty};L^\infty)$$ where $L^{1,\infty}=\sup_{t>0}t f^*(t)$ and $K$ is the Petree K-functional ...
1 vote
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### First-order interpolation inequalities with weights by L.Caffarelli, R.Kohn and L.Nirenberg

L. Caffarelli, R. Kohn and L. Nirenberg showed in this article that, under some conditions, the following weighted interpolation inequality is valid THEOREM: There exists a positive constant $C$ such ...
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### Optimal constant to compare $L^2$ norm of smooth function on $[0, 1]$ to a grid

Suppose that $f \colon [0, 1] \to \mathbb{R}$ is a $C^\infty$ function satisfying the constraints $$f(0) = f'(0) = f(1) = f'(1) = 0, \quad \mbox{and} \quad \int_0^1 (f''(y))^2 \, dy \leq 1.$$ ...
1 vote
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### Regular covering of planar pointsets with convex polygons

Question: What is known about the problem of covering a finite set of $\mathbb{P}$ of points in the plane with convex polygons that have the same number $m$ of points from $\mathbb{P}$ as corners and ...
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### On "canonical" extensions of functions from integers to reals

Although this is essentially a port of my MathSE question, I think the users there tend to not understand how to interpret the questions from a higher perspective (and often too literally). This is ...
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### Equivalent forms of Fourier restriction conjecture

this question is posted in mathstackexchange, but it seems that no one answers it. Sorry to the administrator if this question is not appropriate on Mathoverflow. I'm reading Pertti Maattila's book ...
1 vote
189 views

### Function uniquely determined by its values at integer arguments

A smooth enough, slow growing real-valued function $f(x)$, is uniquely determined by its values at integer arguments. I don't remember the name of the theorem and the conditions for this to be true. ...
66 views

### 3D interpolation function

I've got a 3D figure created using around 30k points and has different regions colored in an specific way according to some unrelated variables that come from a project I'm creating. Taking in ...
1 vote
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### Fastest Implementation of polynomial interpolation?

Suppose I am working over a field $\mathbb{F}$ and have $n$ points in the point-value representation $(x_0,x_1,\cdots,x_{n-1})$. What is the fastest way to do polynomial interpolation and convert this ...
129 views

1 vote