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Lattice Lipschitz operators define a new class of nonlinearBanach-lattice-valued maps that can be written as diagonal functions withrespect to a certain basis. In the $n-$dimensional case, such a map can berepresented 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 meansof lattice Lipschitz operators. The proposed technique is based on theapproximation properties and error bounds obtained for these operators,together with a pointwise version of the interpolation of McShane and Whitneyextension maps that can be applied to almost diagonal functions. In order toget the desired approximation, it is necessary to previously obtain anapproximation to the set of eigenvectors of the original function. We focus onthe explicit computation of error formulas and on illustrative examples topresent our construction.

Approximation of almost diagonal non-linear maps by lattice Lipschitz operators