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Results tagged with polynomials
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user 123142
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.
1
vote
Accepted
Is the difference between polyfits for two data series equivalent to the polyfit of the diff...
At least for interpolation and least square fit the sum of the fit polynomials is equivalent to the fit polynomial of the sum of data points. … For interpolation polynomials it is a consequence of the uniqeuness of the interpolating polynomial. …
- 701
4
votes
Bounds on the smallest real positive root of a polynomial
The structure of the polynomial $P(x)=−ax^q+bx^p−c$, for $a,b,c>0$, $q>p$ is very suitable for analysis with Descartes Rule of Signs.
Since $P(x)$ has two sign changes in its coefficients it can hav …
- 701
2
votes
Accepted
Bounds on the positive roots of a bivariate polynomial
In the system above, for example, the coefficients of the original polynomials are integers and therefore $r_{mn} \geq 1$, i.e., $l_{mn}=1$. … Note that you can always have $r_{mn} \geq 1$ by dividing the original polynomials with the smallest (non-zero) coefficient. …
- 701
3
votes
Cubic curve closest to the given set of points
The method I'll present below, is described (briefly) in the paper "A Revisit to Least Squares Orthogonal Distance Fitting of Parametric Curves and Surfaces" by Liu and Wang. Other methods for solving …
- 701
4
votes
Maximum of a B-spline
Using the recursive derivative formula (see for example here):
$$N'_{i,p}(t) = \frac{p}{t_{i+p}-t_i} N_{i,p-1}(t) - \frac{p}{t_{i+p+1}-t_{i+1}} N_{i+1,p-1}(t)$$
We get that the maximum is achieved whe …
- 701