The Newton Polynomial above can be expressed in a simplified form when are arranged consecutively with equal space. Introducing the notation for each and, the difference can be written as . So the Newton Polynomial above becomes:
is called the Newton Forward Divided Difference Formula.
If the nodes are reordered as, the Newton Polynomial becomes:
If are equally spaced with x= and for, then,
is called the Newton Backward Divided Difference Formula.
Read more about Newton Polynomial: Significance, Addition of New Points, Strengths and Weaknesses of Various Formulae, General Case, Main Idea, Taylor Polynomial, Application
Famous quotes containing the word newton:
“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St Paul’s, like the editions of Balbec and Palmyra.”
—Horace Walpole (1717–1797)