  Lattice Lipschitz operators define a new class of nonlinear
Banach-lattice-valued maps that can be written as diagonal functions with
respect to a certain basis. In the $n-$dimensional case, such a map can be
represented as a vector of size $n$ of real-valued functions of one variable.
In this paper we develop a method to approximate almost diagonal maps by means
of lattice Lipschitz operators. The proposed technique is based on the
approximation properties and error bounds obtained for these operators,
together with a pointwise version of the interpolation of McShane and Whitney
extension maps that can be applied to almost diagonal functions. In order to
get the desired approximation, it is necessary to previously obtain an
approximation to the set of eigenvectors of the original function. We focus on
the explicit computation of error formulas and on illustrative examples to
present our construction.
