Methods

univariate(m::AbstractMonomialLike, l::Integer, dom::Interval)

Compute the Bernstein coefficients of a univariate monomial over an interval.

Input

• m – monomial in one variable
• l – degree of the Bernstein polynomial
• dom – interval domain of the Bernstein expansion

Output

An l+1-dimensional vector that corresponds to the Bernstein expansion of order l of the monomial m.

Notes

For experimental purposes, different variations of the algorithm are available in the internal function _univariate!. By dispatching on any of the following values, you can choose between:

• fastmath : Uses the @fastmath. This is the fastest implementation.
• fastpow : Uses fastpow from DiffEqBase.jl. This is the second fastest implementation.
• base : Uses ^ from Julia. This is the slowest implementation, but it's accuracy is guaranteed to be within an <= 1 ulp for all possible input values.

Algorithm

TODO: add description (ref Smith's PhD thesis).

multivariate(m::AbstractMonomialLike, l::AbstractVector{Int}, dom::IntervalBox{N}) where {N}

Compute the Bernstein coefficients of a multivariate monomial.

Input

• m – monomial in several variables
• l – vector of degrees of the Bernstein polynomial for each variable
• dom – multi-dimensional interval domain of the Bernstein expansion

Output

A vector of vectors holding the Bernstein coefficients implicitly.

Algorithm

TODO: add description (ref Smith's PhD thesis). ```