calculating interpolations (WSOS cone setup) takes too much memory

[chriscoey]

for n > 5, even with very low degree (d = 3), calculating the approximate Fekete points and evaluating the Chebyshev polynomials on them and performing the QR takes too much memory. this is the current method. perhaps using one of the fast multivariate polynomials packages would help. maybe need a different algorithm (at least optionally).

[chriscoey]

another idea is to take log of the point values and then take combinations of them multiplied by the powers, and finally take exp of all these values.

[chriscoey]

JuliaLinearAlgebra/ToeplitzMatrices.jl#38 might help with some aspect of the interpolations (possibly after construction though)

[chriscoey]

note JuliaLang/julia#29846 (comment) QR issues

[chriscoey]

closing due to #110 improving memory usage significantly. worth looking into whether there is a more efficient algorithm for doing the QR of the generalized (for multivariate polynomials) vandermonde matrix transpose.