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Results tagged with polynomial
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user 2488
A mathematical expression w/ >1 term containing the same variable (eg, x & x^2). Polynomials are commonly used to model curvilinear relationships.
2
votes
1
answer
847
views
How to algorithmically determine the best order of fit?
I am doing a least squares polynomial interpolation for 10,000 data sets that look mostly like one period of a sine curve, but whose values are not evenly spaced in the time domain, and can sometimes be …
- 3,132
4
votes
1
answer
1k
views
What is the second derivative of a B-spline?
A B-spline of degree $j$ is defined at knots $\vec k$ by the Cox-de Boor recursion formula
\begin{align}
B_{i,1}(x) &= \left\{
\begin{matrix}
1 & \mathrm{if} \quad k_i \leq x …
- 3,132
6
votes
Accepted
What is the second derivative of a B-spline?
This document gives (with a corrected typo)
\begin{equation}
\frac{\text{d}^{(n)}B_{i,j}(x)}{\text{d}x^{(n)}}
=
(j-1)
\left(
\frac{- \text{d}^{(n-1)} B_{i+1,j-1}(x) / \text{d} …
- 3,132