F. de Belleville ENSICA/TéSA, 1, place Emile Blouin, 31000 Toulouse, FRANCE ENSEEIHT /IRIT, 2, rue Charles Camichel, BP 7122 F 31071 Toulouse, FRANCE L. Dairaine. NICTA, National ICT Australia, Australian Technology Park, Eveleigh NSW 1430, AUSTRALIA ENSICA/TéSA, 1, place Emile Blouin, 31000 Toulouse, France M. Gineste. ENSICA, 1, place Emile Blouin, 31000 Toulouse, France C. Fraboul ENSEEIHT /...

In this paper, we describe the sublattices of some lattices, extending previous results of [Ber]. Our description makes intensive use of graphs.

Adaptive approximation (or interpolation) takes into account local variations in the behavior of the given function, adjusts the approximant depending on it, and hence yields the smaller error of approximation. The question of constructing optimal approximating spline for each function proved to be very hard. In fact, no polynomial time algorithm of adaptive spline approximation can be designed...