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:

“I counted two and seventy stenches,
All well defined and several stinks!
Ye Nymphs that reign o’er sewers and sinks,
The river Rhine, it is well known,
Doth wash your city of Cologne;
But tell me, Nymphs! what power divine
Shall henceforth wash the river Rhine?”
—Samuel Taylor Coleridge (1772–1834)