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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Binary Search Error

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**