Firstly, I am not sure if I am in the right section. Pardon me.(adsbygoogle = window.adsbygoogle || []).push({});

I was reading something related to computational efficiency when evaluating polynomials. Suppose we want to evaluate

[itex]f(x)=1-4 x+6 x^2-4 x^3+x^4[/itex]

it would take n=4 additions and (n^2+n)/2 =10 multiplications to evaluate this f(x) on computer.

We know that it would be better (efficiency and stability) to evaluate f(x) using Horner's method, i.e

[itex]f(x)=1+x (-4+x (6+(-4+x) x))[/itex]

which only take n=4 additions and n=4 multiplications on the computer, (i.e. round-off error will be minimised).

So here is my question: wouldn't it better to evaluate

[itex]f(x)=(x-1)^4[/itex]

since it would only need 1 addition and 4 multiplication?

Could anyone share some insights on this?

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# Horner's method vs (x-1)^n

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