GENERAL DIVIDED DIFFERENCE POLYNOMIAL INTERPOLATION FORMULA: A NEW APPROACH

Abstract

In this paper, a simple introduction about the interpolation method and the new approach of
(forward) divided differences are given when the arguments are unevenly spaced. These
divided differences are carried out and applied to develop a new polynomial interpolation
formula. In accordance with idea of these new (forward) divided differences, the leading
differences can be deduced when the arguments are evenly spaced. In the development of
the new divided difference table, the advantages are showed according to the speedup of
human labour and efficiency. Finally, to implement the new approach via computer an
algorithm and FORTRAN77 program are carried out to construct the new divided
differences for a given data points and to estimate the value of a function at any tabulated
or non-tabulated points.