In this chapter, we study numerical techniques that deal with given set of
data points arising from experimental works. Starting from linear interpolation,
different interpolating polynomials are discussed that are used to find functional value
at intermediate points of the given data set. Lagrange interpolation is discussed that
does not require equally spaced data points. Newton forward and backward difference
interpolation formulae are derived to evaluate function near the beginning and end
parts of the given data sets. Linear least-squares fit that is widely used to approximate
unknown functions is presented and an algorithm is developed. We also discuss least-squares approximations for approximating an explicit function on given interval.
Keywords: Interpolation, Extrapolation, Polynomial curve fitting, Approximation.
