• A NOTE ON POLYNOMIAL INTERPOLATION FORMULAE

Abstract

Through introducing a formula for divided difference and new schemes of divided difference tables, we study an interpolation formula, which generalizes both Newton and Lagrange interpolation formula to use interpolants that fit the derivatives, as well as the function values for arbitrary spaced grids. Using this, we derive other interpolation formulas, in terms of differences and divided differences for evenly spaced data. Comparing with former polynomial interpolation formulas, these new formulas have some new featured advantages for approximating functional values for evenly and unevenly spaced data.