Studies on Functional Approximations in Numerical Analysis

In this work I have discussed most effective approximating functional forms.Both in Econometric and in numerical problems,the need for and approximating function often arises.One possibility is that one has finite set of data points and wants to determine underlying functional form.By using different methods I have discussed it properly.With an approximating functional form - one can find function value much quicker.In this paper, smart approximation theory such as Spline approximation,Least-Square approximation,Pade,Rational approximations and there comparative study also shown properly. At the end of the chapter the inestimable importance in mathematics - Fourier approximation and Fast Fourier transform(FFT) are also described.