Interpolation by ridge polynomials and its application in neural networks

We consider multivariate interpolation at arbitrary points and provide effective interpolation formulas by using simple ridge polynomials which essentially possess the nature of univariate polynomials in computation, and show that ridge polynomials with least degree can be found for interpolation purpose, which a computational algorithm is provided correspondingly. We then apply the interpolation results to design a computational algorithm for training feedforward neural networks.