Newton Polynomial

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

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