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Results tagged with polynomials
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user 132216
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
4
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1
answer
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Marsden's Identity and B-splines
But when I do that, I don't really see how this expression describes all possible polynomials of degree $k-1$. … Doesn't $(\cdot -\tau)^{k-1}$ represents all polynomials of degree
$k-1$ where $\tau$ is a root with multiplicity $k-1$?
Am I missing something here? …
- 515
2
votes
Accepted
Marsden's Identity and B-splines
<\tau_k$, is a basis for the space $\Pi_{<k}$ (the space of polynomials of degree smaller than $k$). … Hence any polynomials of degree $<k$ can be written as a linear combination of the elements in the basis, i.e.:
$$\beta_1(\cdot-\tau_1)^{k-1}+... …
- 515