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# Tag Info

Accepted

### Do splines preserve monotonicity?

I assume you mean nondecreasing, i.e., monotonically increasing. If so, the answer is "no." For example, interpolate (0,0), (1,10) and (2,11) with a natural cubic spline:
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### Sign of 3j symbol (in view of interpolation)

Wolfram contains the following formula which should make your calculations easy: If $\ell_1+\ell_2+\ell_3=2g$ then $$\begin{pmatrix} \ell_1 &\ell_2 &\ell_3\\ 0&0&0 \end{pmatrix}=$$ ...

### Interpolation space between $L^1\cap L^2$ and $L^1$

In the case of a set of finite measure (Bourgain in the quoted paper deals with the case of finite measure (torus)) we have that $\Vert f\Vert_1\leq C\Vert f\Vert_2$ so we actually have $(\infty,1)$ ...
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### Interpolation space between $L^1\cap L^2$ and $L^1$

As requested, I post my comment as an answer (although this is not a true answer, just a possibly useful reference; feel free to edit it if this approach works out). In Section 3 of the article ...

### Does every positive continuous function have a non-negative interpolating polynomial of every degree?

I think I can prove the following : For every continuous function $f:[a,b]\to (0,\infty)$, $\exists n_0>1$ such that for every $n\ge n_0$, there are $n+1$ distinct points in $[a,b]$ such that the ...

### Does every positive continuous function have a non-negative interpolating polynomial of every degree?

This question was recently studied in that paper: F. Charles, M. Campos-Pinto, B. Després, Algorithms for positive polynomial approximation, hal-01527763, assuming that the function $f$ is Lipschitz ...
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### About Newton's forward and backward interpolation

The forward and backward finite differences and the derivative lower the degree of a polynomial by one. This property underlies the construction of series expansions of polynomials and, therefore, ...
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### Fastest Implementation of polynomial interpolation?

Polynomial interpolation can be done via multiplying a Vandermonde matrix (or its inverse) by your coefficient/evaluation vector --- it is a change of basis on the vector space of polynomials of ...