Since it’s not so obvious what the
Wilkinson package does from the current README, here is an example. The new generalized Wilkinson-type error bound I proved in my paper allows the prediction of a round off error bound for any type of polynomial form (previously only the Horner form and Basis forms have been investigated). Here is what this looks like with actual data generated with
Wilkinson in Julia
Shown below is the predicted error bound for the round off error of a polynomial, and also the actual round off error computed using polynomial evaluation normalized by arbitrary precision float for comparison.
Using the table below, I am able to make predictions about what is the most optimal form of a polynomial, satisfying both the least Wilkinson-type error bound and also minimal memory usage, etc.
The main result is a new characteristic method, which is able to predict the ordering of the polynomial forms in terms of the generalized Wilkinson-type round off error bound, which is enabled by Julia AST.
This research discovery would not have happened if Julia did not exist, because then I wouldn’t have been messing around with this kind of thing using the Julia abstract syntax tree (AST) representations.
You can read a draft of the paper here: https://github.com/chakravala/Wilkinson.jl/wiki/poly.pdf
So, thank you for the Julia AST, which led me to this discovery, which is also related to James H. Wilkinson, whom I also referenced in my paper.