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Results tagged with splines
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user 490264
Splines and their properties and applications. A spline is a function defined piecewise by polynomials, and is typically used in interpolating problems.
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Abstract algebraic link between two problems involving polynomials and (generalized) Vanderm...
When studying the theory of splines, I came across the following Proposition: the family of polynomials
$$\Big\{\binom{N}{j} (X+\alpha_i)^{N-j}\Big\}_{i=0\dots L,\; j=0\dots k_i}$$
is always free (and …
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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 …
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Proof that elements of Beppo-Levi-like spaces are functions (and not just distributions)?
After some more thought, I gave up Meinguet's approach above (based on sums of the form $\sum_j c_j\tau_{x_j}f$) for a more direct approach in order to prove continuity of the elements of $H$. Any fee …
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Proof that elements of Beppo-Levi-like spaces are functions (and not just distributions)?
This is a direct generalization of the Beppo-Levi spaces which underlie thin-plate splines interpolation, as described e.g. by Duchon [1], Meinguet [2], Wahba [3], etc., and that correspond to taking $ … [1] Duchon, Jean, Splines minimizing rotation-invariant semi-norms in Sobolev spaces, Constr. Theory Funct. several Variables, Proc. Conf. Oberwolfach 1976, Lect. Notes Math. 571, 85-100 (1977). …