A New (Proposed) Formula for Interpolation and Comparison with Existing Formula of Interpolation

Abstract

The word “interpolation” originates from the Latin verb interpolare, a contraction of “inter,” meaning “between,” and “polare,” meaning “to polish.” That is to say, to smooth in between given pieces of information. A number of different methods have been developed to construct useful interpolation formulas for evenly and unevenly spaced points. The aim of this paper is to develop a central difference interpolation formula which is derived from Gauss’s Backward Formula and another formula in which we retreat the subscripts in Gauss’s Forward Formula by one unit and replacing by . Also, we make the comparisons of the developed interpolation formula with the existing interpolation formulas based on differences. Results show that the new formula is very efficient and posses good accuracy for evaluating functional values between given data.

Keywords: Interpolation, Central Difference, Gauss’s Formula.