Interpolation

Abstract

Polynomials have attracted the attention of mathematicians for centuries because of their many beautiful properties. For numerical purposes they have the advantage that their computation reduces to additions and multiplications only. Therefore, it is quite natural to use polynomials for the approximation of more complicated functions. A classical approach to specifying the coefficients of a polynomial of degreen isto prescribe that its values atn+ 1 distinct points coincide with those of the function to be approximated. The development and investigation of such interpolation polynomials has a long mathematical history, beginning with the use of the method of interpolation to tabulate the logarithms, as proposed by Briggs in the early seventeenth century.