Nested Scheme (Help, I need a definition/explanation)

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SUMMARY

The discussion centers on the nested scheme, also known as Horner's scheme, which is a method for efficiently evaluating polynomials. The user seeks a clear definition and explanation of this technique, as their math book lacks rigorous definitions. An example provided illustrates how the polynomial f(x) = 2x³ - 6x² + 2x - 1 can be rewritten using Horner's scheme for more efficient computation. The discussion highlights the need for better resources and explanations regarding this mathematical method.

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Atran
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Hi, I'm reading about polynomials and I've encountered a method called nested scheme.
The tragedy is that my math book usually has no rigorous definitions and sometimes lacks definitions.
My book is only stating that nested scheme is a method for evaluating polynomials, and thereafter it continues with two examples. It does not provide an explanation.

I cannot find any proper link, for nested scheme, in google. Can you teach me the very basics, and that should be sufficient for the understanding of more advanced topics...
Thanks for help...
 
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This sounds like something that is called Horner scheme, a technique for evaluating polynomials efficiently.

For example, f(x) = 2x3 - 6x2 + 2x - 1 can be rewritten as f(x) = x(x(2x - 6) + 2) - 1.

More information here - http://en.wikipedia.org/wiki/Horner_scheme
 
Thanks...
 

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