INTERPOLATION AND CURVE FITTING

This chapter deals with interpolation and curve fitting. It considers interpolation by Lagrange polynomial and Newton polynomial and a polynomial approximation problem of finding a polynomial close to a given function. Once the target points have been fixed, it is nothing but an interpolation problem that can be solved by the Lagrange or Newton polynomial. The chapter explores how to choose the target points for better approximation, rather than taking equidistant points along the x-axis. It also considers pade approximation by rational function and interpolation by cubic spline. In some cases, we need to find the polynomial function that not only passes through the given points but also has the specified derivatives at every data point. Such a polynomial is said to be the Hermite interpolating polynomial or the osculating polynomial. The chapter also deals with only the simplest way of two-dimensional interpolation, that is, a generalization of piecewise linear interpolation called the bilinear interpolation.