JuliaApproximation
Generalized eigenvalue problems on a disc
Timon @TSGut has done the heavy lifting and has implemented Jacobi matrices for Zernike polynomials on a disc.
Alberto @APaganini could you remind us what exactly you required? If I remember correctly, as a first step you wanted to solve
-Laplace(u)(x,y) = q(x,y) u(x,y)
on a disc with zero Dirichlet bcs. What should we pick for q(x,y)? (@dlfivefifty)
Amazing, many thanks for your help! The function q I'm interested in is
q(x,y) = (1 + |g(x+iy)|^2)^2
where g(z) is a polynomial with real coefficients in the complex variable z.
Yes, we don't need anything more complicated than that. In a next step we may be brave and even try rational functions (but I first have to think about what having poles in the disc would mean for the specific application).