Please explain the thoery of Newtons Interpolating polynumerals?

Answer 1

Do you mean the theory of Newton's Interpolating polynomials?

Answer 2

In the mathematical field of numerical analysis, a Newton polynomial, named after its inventor Isaac Newton, is the interpolation polynomial for a given set of data points in the Newton form. The Newton polynomial is sometimes called Newton's divided differences interpolation polynomial because the coefficients of the polynomial are calculated using divided differences.
As there is only one interpolation polynomial for a given set of data points it is a bit misleading to call the polynomial Newton interpolation polynomial. The more precise name is interpolation polynomial in the Newton form.

Answer 3

http://en.wikipedia.org/wiki/Newton_polynomial