ON A NEW STABLE AND ORTHONORMAL BASISEFOR REPRODUCING KERNELS

In the current work an interesting strategy will begiven to overcome the ill-conditioning of linear systems arising frommultivariate radial basis function interpolation methods. For this atechnique based on the well-known Newton s interpolation formula,using generalized divided di erences will be adopted to constructnew well-behaving bases based on the radial basis function. The re-sulting basis turns out to be orthogonal in the radial basis functionnative Hilbert space, and the interpolation technique based on thegenerated basis are more stable than before. In nal a numericalexample is presented to show the accuracy of the method.