Probably the most important advantage of the discrete variable representation (DVR) is its simplicity. The DVR potential energy matrix is constructed directly from the potential function without evaluating integrals. For simple kinetic energy operators the DVR kinetic energy matrix is determined from transformation matrices and exact matrix representations of one-dimensional kinetic energy operators in the original delocalized polynomial basis set. For complicated kinetic energy operators, for which matrix elements of terms or factors with derivatives must be calculated numerically, defining a DVR is harder. A DVR may be defined from a finite basis representation (FBR) where matrix elements of terms or factors in the kinetic energy operator are computed by quadrature but implicating quadrature undermines the simplicity and convenience of the DVR. One may bypass quadrature by replacing the matrix representation of each kinetic energy operator term with a product of matrix representations. This product approximation may spoil the Hermiticity of the Hamiltonian matrix. In this paper we discuss the use of the product approximation to obtain DVRs of complicated, general kinetic energy operators and devise a product scheme which always yields an Hermitian DVR matrix. We test our ideas on several one-dimensional model Hamiltonians and apply them to the Pekeris coordinate Hamiltonian to compute vibrational energy levels of H-3(+). The Pekeris coordinate Hamiltonian seems to be efficient for H-3(+). We use Jacobi polynomial basis sets and derive exact matrix elements for (d/dx) G(x)(d/dx), r(x)(d/dx), r(x), and (1-x)(lambda)e(-xt) with G(x) and r(x) rational functions. We discuss the utility of several Jacobi DVRs and introduce an improved FBR for general kinetic energy operators with more quadrature points than basis functions. We also calculate Euclidean norms of matrices to evaluate the accuracy of DVRs and FBRs.