We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown values is interpolation on a discrete graph structure. From the discrete graph structure, we build a refined approximation to the function over its domain. This fine approximation can then be used for problems such as optimization, which we illustrate by identifying local minima.

翻译：我们考虑将一维实值函数离散化为图的问题。目标是找到一组小规模的点集，并基于这些点集近似其余函数值。对未知值的近似方法是在离散图结构上进行插值。通过该离散图结构，我们构建出函数在其定义域上的精细近似。该精细近似可用于优化等问题，我们通过识别局部最小值对此加以说明。