Stable evaluation of box-splines. The author proposes and investigates a new modification of the well-known de Boor’s recursive algorithm for the evaluation of box-splines. A careful analysis of computational complexity, numerical stability/instability of the recursive algorithm and some steps in its optimization allow a reformulation which can overcome existing numerical difficulties without losing efficiency. Finally a concise vectorized MATLAB-implementation of the proposed method is given. (netlib numeralg na11)