6.1 The Power Form versus the Newton Form

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	Java Number Cruncher: The Java Programmer's Guide to Numerical Computing By Ronald  Mak
	Table of Contents
	Chapter  6.   Interpolation and Approximation

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6.1 The Power Form versus the Newton Form

We are familiar with the power form of a polynomial of degree n:

We'll use the subscript n after the name of the function to indicate the function's degree, its highest exponent of x.

Another polynomial form is the Newton form:

which is computationally convenient because of the way the ( x - x _i ) products accumulate from one term to the next?awe simply multiply the previous product by the next ( x - x _i ). The x _i constants are called centers. We'll use the Newton form to represent polynomial interpolation functions. ^[1]

^[1] The Newton form is actually equivalent to the power form, which you can discover by multiplying out the terms and reorganizing them. And, yes, this is the same Isaac Newton of the algorithm for finding roots described in Chapter 5.

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