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:

“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)