Vandermonde inverse

[nsajko]

Here I have a module with a short and simple implementation of a Vandermonde matrix inverse:

https://gitlab.com/nsajko/PolynomialPassingThroughIntervals.jl/-/blob/main/src/VandermondeInverse.jl

The module depends on the SkipVectors module, located in the same directory.

As far as I remember VandermondeInverse.vandermonde_inv offers a huge improvement in accuracy over using SpecialMatrices.jl, and sometimes it's significantly faster, too.

Do you want a PR? If so, do you have any suggestions regarding the code, or testing, or perhaps do you want some benchmarks?

[JeffFessler]

Sure it would be good to have a fast inv here for Vandermonde.
I actually don't see any inv in the current code (I haven't worked the guts of the Vandermonde case so I don't know much about the internals), so yes it would be be helpful to see a benchmark to see exactly what you are comparing. Oh, perhaps what you are calling inv is actually A\b. Consider using the standard Julia names like ldiv!

Comments on code:

• for subtracter you might look at Base.Fix1
• do you really need all those local statements? you need those in a REPL, but i don't think they are needed in functions.
• i don't understand vandermonde_inv(x::AbstractVector{T}) - a docstring might help
• please include docstrings and tests.