Polynomials and Interpolations

Abstract

If selected values of a function are given in a tabular representation, it is often desirable to obtain an easily computable formula which yields both those given values and approximations for in-between points, not included in the table. This procedure is called interpolation. In this chapter, we obtain formulas of Lagrange and Newton for polynomials which accomplish this interpolation. This necessitates the study of the factorization of polynomials. Finally, we study the approximation by polynomials of a function defined on a closed interval.