8.2.3 newton formm a more generalized form of the shifted power form is newton form p(x)=a, +a,(x-c)+a,(x-c,)(x-c,)+..+a, (x-c(x-c)(x-c,) this form plays a vita

8.2.3 Newton Formm A more generalized form of the shifted power form is Newton form P(x)=a, +a,(x-c)+a,(x-c,)(x-c,)+..+a, (x-c(x-c)(x-c,) This form plays a vital role in the interpolation theory. Newton form becomes shifted power form for the values c, =c, =...c, = C, and further power form for the value c = 0. 8.2.4 Nested Newton Form In Newton form of the polynomial of degree n, the total number of multiplications and additions are "(n+1) and n+ n(n+1) , respectively. It will be better to use the following 2 2 nested Newton form to minimize the number of arithmetic operations.