The absorbing boundary conditions defined on the interface between the sub-domains are of major importance for the convergence of domain decomposition methods. In linear elasticity, optimal absorbing boundary conditions can be derived and are associated with a Dirichlet-to-Neumann map. In this paper, several original algebraic techniques of approximation of this Dirichlet-to-Neumann map are investigated. Asymptotic, spectral and numerical analysis of these techniques are successively presented for linear elasticity problems. Various numerical experiments illustrate the convergence properties of these original techniques.