ABSTRACT
The focus of our discussions in the previous chapters has been the question of approximation of a given continuous function f, defined on an interval [a,b] by a polynomial on that interval either through Lagrange interpolation, β-Lagrange interpolation, Hermite interpolation or ²-Hermite interpolation polynomials. Each of these constructions was global in nature, in the sense that the approximation was defined by the same analytical expression on the whole interval [a,b]. In this chapter, we will present an alternative and more flexible way for approximation of a function f and this approach is based on the dividing the interval [a,b] into a number of subintervals and to look for a piecewise approximation by polynomials of low degree. Such piecewise-polynomial approximations are called splines, and the endpoints of the subintervals are known as the knots.
