ABSTRACT
Many interpolants serve only to predict the value at the given interpolation points. For more flexibility, learning systems integrate regularization, a technique for smoothing across the data. Several of the interpolation techniques presented in the chapter depend on special families of functions. This chapter focuses on the connection between these special families and linear algebra concepts. The Hermite polynomials are also an important family of functions that arise in probability theory. It presents Lagrange interpolating polynomials which fit exactly to a given set of interpolating points. Runge's phenomenon occurs with polynomial interpolants of high degree over a set of equally spaced interpolation points. Runge's phenomenon is when the interpolant matches the desired function or data extremely well in the middle of the interpolation interval and begins to oscillate at the edges of the interval. There are many techniques for sending an encrypted code and decrypting that code.
