I have written a computer program that uses binary search to find the root to f(x) = 0, where f is an arbitrary (user-defined) function.(adsbygoogle = window.adsbygoogle || []).push({});

If the rounding error [tex]\leq \epsilon[/tex] and the truncation error [tex]\leq \delta[/tex], what is the estimated accuracy of the output?

Would the following reasoning be correct?

Let [tex]r[/tex] be s.t. [tex]f(r) = 0[/tex]. Then [tex]f(x) = f(r) + (x-r)f'(r) + O((x-r)^2)[/tex]. So the estimated error is [tex]|x-r| \approx |\frac{f(x)}{f'(r)}| = \frac{\epsilon+\delta}{|f'(r)|}[/tex]?

Thanks.

Edited: I meant expanded till the divisor is NOT 0.

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# Binary Search Error

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