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Results tagged with interpolation
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user 490264
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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Abstract algebraic link between two problems involving polynomials and (generalized) Vanderm...
I noticed that the two following results, both in the field of polynomial interpolation, involve Vandermonde matrices, or their generalization known as confluent Vandermonde matrices (better explained … here if you have access):
Generalized Hermite Interpolation solves the following linear system over polynomials $P\in\mathbb R_N[X]$ :
$$\forall i=0\dots L,\quad \forall j=0\dots k_i,\quad \frac1{j!} …
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Abstract algebraic link between two problems involving polynomials and (generalized) Vanderm...
Well, after some more thinking I'm going to answer my own question. It was pretty much just a matter of linking all elements together.
Here are my notations, in $\mathbb R_N[X]$.
Note $\partial$ the …