Because I was a (tiny) bit unsatisfied with the Polynomial package,
I wrote my own polynomial functions, like
- polyval() to be applied to vectors as well as polynomial types
- roots() that uses the Matlab order in constructing the companion
matrix and finding all roots
- horner() that utilizes the Horner scheme to compute the value
and the derivative of the polynomial at the same time
(useful for a specialized version of Newton's algorithm)
- a deflated Horner function to return p(x) = (x - x0)*q(x) when
x is a root of polynomial p
- polyfit() for fitting polynomials to data, etc.
I think a polyfit() function should in any case be a part of a polynomial
package. (Is such a function contained in any other package?)
Besides that an implementation of the Muller algorithm for computing zeros
of
polynomials might be helpful. Or the calculation of the number of real roots
of a polynomial in an interval (Descartes' and Sturm's rules). There is
more
interesting numerical stuff that could be part of such a polynomial package.
On Thursday, May 8, 2014 3:42:03 AM UTC+2, Tony Kelman wrote:
>
> Yes, Polynomial is using a different convention than Matlab or what you
> used below in how it constructs the companion matrix. Polynomials.jl uses
> yet another convention. Both produce more accurate (comparable to Matlab)
> results for the roots of the Wilkinson polynomial if you just switch the
> indices during construction of the companion matrix. See
> https://github.com/vtjnash/Polynomial.jl/blob/master/src/Polynomial.jl#L350-L353for
> Polynomial, or
> https://github.com/loladiro/Polynomials.jl/blob/master/src/Polynomials.jl#L324-L325for
> Polynomials.
>
> I think the intent (see https://github.com/vtjnash/Polynomial.jl/issues/5)
> is to deprecate Polynomial and switch the coefficient order by developing
> under the Polynomials name going forward, but Keno's probably been too busy
> to register the new package, turn on issues, etc. I'm doing some work on
> piecewise stuff in a branch of Polynomials, I might just adopt the package.
> I know David de Laat has put together packages for sparse multivariate
> polynomials https://github.com/daviddelaat/MultiPoly.jl and orthogonal
> polynomials https://github.com/daviddelaat/Orthopolys.jl, don't think
> they're registered but it might make sense to eventually unify all of these
> into the same package.
>
