Lagrange-Lobatto interpolating polynomials in the discrete variable representation

The discrete variable representation (DVR) is a well known and widely used computational technique in many areas of physics. Recently, the Lagrange-Lobatto basis has attracted increasing attention, especially for radial Hamiltonians with a singular potential at the origin and finite element DVR constructions. However, unlike standard DVR functions, the Lagrange-Lobatto basis functions are not orthogonal. The overlap matrix is usually approximated as the identity using the same quadrature approximation as for the potential. Based on the special properties of overlap matrix of Lagrange-Lobatto polynomials, an explanation of the success of the identity approximation, including error bounds, is presented. Results for hydrogen and the more nontrivial potentials of self-consistent all-electron density functional atomic calculations are also given.