Radial basis functions are a simple and accurate method for multivariate interpolation but the ill-conditioning situation due to their interpolation matrices, discourages an acceptable approximation for both large number of nodes or flat function interpolation. In current work, a new type of basis named well-conditioned RBFs (WRBFs) was created by adding the strictly positive definite Radial Basis Functions (SPD-RBFs) to cardinal functions, was introduced and applied for interpolation. To light up this manner, two classes of global cardinal functions were used for adding by SPD-RBFs. These cardinal functions are Shepard functions and Quasi-cardinal RBFs. Theoretical and numerical analyses prove that utilizing WRBFs has some advantages such as eliminating the ill-conditioning system which has arisen from the global positive definite RBFs interpolation, improving the convergence of pure cardinal functions interpolation and also working better than pure RBFs for small shape parameters.

径向基函数是用于多元插值的一种简单而准确的方法，但是由于其插值矩阵而导致的状况不佳，不利于为大量节点或平面函数插值提供可接受的近似值。在当前的工作中，通过向基数函数中添加严格的正定径向基函数（SPD-RBFs），创建了一种称为良好条件的RBF（WRBF）的新型基础，并将其应用于插值。为了点亮这种方式，SPD-RBF使用了两类全局基数函数进行添加。这些主要功能是Shepard功能和准基本RBF。