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.

翻译：格Lipschitz算子定义了一类新的非线性Banach格值映射，其可表示为关于特定基的对角函数。在$n$维情形下，此类映射可表示为$n$个一元实值函数构成的向量。本文发展了一种利用格Lipschitz算子逼近近似对角映射的方法。所提出的技术基于这些算子获得的逼近性质与误差界，同时结合可应用于近似对角函数的McShane与Whitney延拓映射的点态插值版本。为获得所需逼近，需预先获取原始函数特征向量集的逼近。我们聚焦于误差公式的显式计算与说明性示例以展示构造方法。