Question

Are newton interpolation formula and taylor series realted ?

Answer 1

no they are not similar

Answer 2

The general form of Taylor's theorem for a function f:K→K" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.4px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">f:K→K, where K is the real line or the complex plane, gives the formula, f=Pn+Rn, where Pn is the Newton interpolating polynomial computed with respect to a confluent vector of nodes, and Rn is the remainder. Whenever f′≠0, for each m=2,…,n+1, we describe a “determinantal interpolation formula”, f=Pm,n+Rm,n, where Pm,n is a rational function in x and f itself. These formulas play a dual role in the approximation of f or its inverse.