New bases from old: measure modification, semiclassical Jacobi families, and classical bases on triangles, disks and annuli.
Polynomial measure modification, with connection matrices as banded Cholesky factors of Gram matrices.
Semiclassical Jacobi families for \(x^a(1-x)^b(t-x)^c\), with sparse conversion, differentiation, and Cholesky/QR hierarchy construction.
Classical orthogonal polynomials on squares, triangles and disks, built by separation of variables.
Zernike-type bases on the annulus, a sparse Laplacian, and a convergent Galerkin solver for the Dirichlet problem.
Gram factors, polynomial modification and degree-block bandwidth.
Separated bases, family-preserving modifications and their connection support.
Exact zeros, parity sectors and obstructions to uniform inner bandwidth.
Cartesian disk systems, normalized connections and exact finite sections.