polynomial-0.6.5: Polynomials

Math.Polynomial.Lagrange

Synopsis

Documentation

lagrangeBasis :: (Fractional a, Eq a) => [a] -> [Poly a]Source

Returns the Lagrange basis set of polynomials associated with a set of points. This is the set of polynomials each of which is 1 at its corresponding point in the input list and 0 at all others.

These polynomials are especially convenient, mathematically, for interpolation. The interpolating polynomial for a set of points (x,y) is given by using the ys as coefficients for the basis given by lagrangeBasis xs. Computationally, this is not an especially stable procedure though. Math.Polynomial.Interpolation.lagrangePolyFit implements a slightly better algorithm based on the same idea.

Generally it is better to not compute the coefficients at all. Math.Polynomial.Interpolation.polyInterp evaluates the interpolating polynomial directly, and is both quicker and more stable than any method I know of that computes the coefficients.

lagrange :: (Num a, Eq a) => [a] -> Poly aSource

Construct the Lagrange master polynomial for the Lagrange barycentric form: That is, the monic polynomial with a root at each point in the input list.

lagrangeWeights :: Fractional a => [a] -> [a]Source

Compute the weights associated with each abscissa in the Lagrange barycentric form.