Ridge polynomials (on the disk)?

JuliaApproximation / MultivariateOrthogonalPolynomials.jl

Supports approximating functions and solving differential equations on various higher dimensional domains such as disks and triangles

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Open MikaelSlevinsky opened 3 years ago

MikaelSlevinsky commented 3 years ago

These look like P_{n,k}(x,y) = U_n(x * cos(k*pi/(n+1)) + y * sin(k*pi/(n+1))), orthogonal on the unweighted unit disk.

Sparse differentiation is trivial (using ultraspherical generalizations), but the Jacobi operators are not obvious.

MikaelSlevinsky commented 3 years ago

dlfivefifty commented 3 years ago

Yes I know this family from Dunkl and Xu, it’s cool and doesn’t require any high order OPs