Shifted Interpolation Methods for Efficient Resolution of Algebraic and Transcendental Equations

Abstract

A popular method in mathematics and statistics for determining values between any two points is interpolation. For both equally and unequally spaced data sets, numerous techniques have been employed to derive practical interpolation equations. This work aims to develop a difference interpolation formula derived from Gauss's Formula and another formula where we substituted  for  and reused the subscript in Gauss's Forward Formula by four units. Additionally, based on the differences, we compared the generated interpolation formula with the current interpolation formulae. We discovered from the error analysis that the new formula we obtained is significantly more accurate and efficient at resolving functional values between the provided data.