The mapped bases or Fake Nodes Approach (FNA), introduced in [10], allows to change the set of nodes without the need of resampling the function. Such scheme has been successfully applied in preventing the appearance of the Gibbs phenomenon when interpolating discontinuous functions. However, the originally proposed S-Gibbs map suffers of a subtle instability when the interpolant is constructed at equidistant nodes, due to the Runge's phenomenon. Here, we propose a novel approach, termed Gibbs-Runge-Avoiding Stable Polynomial Approximation (GRASPA), where both Runge's and Gibbs phenomena are mitigated. After providing a theoretical analysis of the Lebesgue constant associated to the mapped nodes, we test the new approach by performing different numerical experiments which confirm the theoretical findings.

翻译：在[10] 中引入的地图基础或假节点方法(FNA)允许改变一组节点,而无需重新标出功能。这种办法成功地用于防止在互调不连续函数时出现Gibs现象。然而,最初提议的S-Gibbs地图由于龙格现象,在等离子节点上建造了内插器,因此出现了微妙的不稳定。在这里,我们提出了一个新颖的办法,称为Gibbbs-Runge-Aviing Stable Poltinomical Approximation(GRASPA),即减少Runge和Gibs现象。在对与所绘制节点相关的Lebesgue常数进行理论分析之后,我们通过进行不同的数字实验来测试新办法,以证实理论结果。