Newton Polynomial - Taylor Polynomial

Taylor Polynomial

The limit of the Newton polynomial if all nodes coincide is a Taylor polynomial, because the divided differences become derivatives.

 \lim_{(x_0,\dots,x_n)\to(z,\dots,z)} f + f\cdot(\xi-x_0) + \dots + f\cdot(\xi-x_0)\cdot\dots\cdot(\xi-x_{n-1})
 = f(z) + f'(z)\cdot(\xi-z) + \dots + \frac{f^{(n)}(z)}{n!}\cdot(\xi-z)^n

Read more about this topic:  Newton Polynomial

Famous quotes containing the word taylor:

    Let’s just call what happened in the eighties the reclamation of motherhood . . . by women I knew and loved, hard-driving women with major careers who were after not just babies per se or motherhood per se, but after a reconciliation with their memories of their own mothers. So having a baby wasn’t just having a baby. It became a major healing.
    —Anne Taylor Fleming (20th century)