Error inequalities in quintic discrete hermite interpolation - Yarraguntla Sambasiva Rao (2009)
Interpolation is the method of finding a polynomial whose graph will pass through a given set of points (x, y). the purpose of using interpolation is to approximate complex function to a simpler polynomial which is easer to integrate or differentiate. Generally, the complex function can be converted into a simpler form my means of different methods of interpolation. Some of the interpolation methods are Polynomial interpolation, Piecewise cubic interpolation and Hermite interpolation, etc. based on how important the information is, one can choose which interpolation technique to apply. The interpolation technique discussed in this project is quintic discrete Hermite interpolation which is an extension of cubic discrete Hermite interpolation. The current project deals with the derivation of explicit expression for quintic discrete Hermite interpolation. The error inequalities in quintic discrete Hermite interpolation are then successfully derived by means of Peano’s kernel theorem.