Numerical Analysis Questions & Answers  


I'm not sure why you're getting negative bits.. You have more or less the right logic thus (although not perfectly). Keep working more on it.




I will answer your question if the numbers are properly typeset. Answer it again below and use LATEX to write the math and numbers properly.






Yes, the relative error can be less than $\epsilon_{\rm mach}$. In class, $\epsilon_{\rm mach}$ was defined as the maximum relative error on a nondenormal float. For most nondenormal floats, the error will of course be less. 1 point bonus boost.




Yes, of course, the number of iterations will depend on the initial interval chosen. This is why the initial interval is specified in the question. There are no rules that can be used to guess a proper initial interval that would apply in the general case because each function has a different behaviour. But if you do know the function, then it may be possible to specify an initial interval that is quite close to the root through a good guess for the root. 1 point bonus boost.



$\pi$ 