Abstract:
In this thesis we have studied phenomenon associated with interpolation of equally
spaced data known as Runge phenomenon. This phenomenon was first observed by
Carl David Tolme Runge which deals with the oscillatory behavior of a higher degree
interpolating polynomial near the end points of equally spaced data.
In this dissertation we have discussed the conditions for the occurrence or absence of
this phenomenon and illustrated our results graphically. Aasimpleaproofafor theacaseaof
Runge functionaona[a; a] has been discussed. A simple formula has been found to
calculate the point, for a fixed a, beyond which Runge phenomenon makes its appearance.
The role of Chebyshev polynomials in approximation theory has been briefly discussed.
To further improve the convergence rate and the reduction of an error obtained through
approximation of an interpolating polynomial and non-polynomial function different
types of notions like Fourier series and Chebyshev series were discussed.
