Abstract It is well-known that the finite difference discretization of Laplacian eigenvalue problem ? ?u = ?u leads to a matrix (EVP) Ax ?x where A Toeplitz-plus-Hankel. Analytical solutions tridiagonal matrices with various boundary conditions are given in recent work Strang and MacNamara. We generalize results develop analytical certain generalized problems (GEVPs) ?Bx which arise from elemen...