Lagrange functions are localized bases that have many applications in signal processing and data approximation. Their structure and fast decay make them excellent tools for constructing approximations. Here, we propose perturbations of Lagrange functions on graphs that maintain the nice properties of Lagrange functions while also having the added benefit of being locally supported. Moreover, their local construction means that they can be computed in parallel, and they are easily implemented via quasi-interpolation.

翻译： Laggrange 函数是局部基点, 它在信号处理和数据近似方面有许多应用。 它们的结构和快速衰变使得它们成为构建近似值的绝佳工具。 在这里, 我们提议在图表上对 Laggrange 函数进行扰动, 以维持 Laggrange 函数的好特性, 同时也具有当地支持的额外好处 。 此外, 它们的地方建设意味着它们可以平行计算, 并且很容易通过准内插执行 。