Numerical Analysis Questions & Answers  


No attached pictures are allowed in the QNA thread except if they are drawings. The mathematics must be typeset within your question using LATEX, not using pictures.






I don't understand the question fully. If I ask for the smallest positive number, then this can not be zero whether the number is normal or denormal because zero is not positive. I'll give you just 0.5 point bonus boost because you should put your question in more context so that I can understand better what you mean.




When using float variables in C, $\epsilon_{\rm mach}$ should be set to $6\times 10^{8}$. But I won't take away points if you use a slightly more conservative value of $10^{7}$. The order of magnitude is what counts here. It was a good question, I'll give you 1.5 points bonus boost for it.




No, this should read: $$ \epsilon_{\rm mach}=\frac{1+2^{24}1}{1} $$ The first two terms on the numerator $1+2^{24}$ correspond to the sum of the smallest number 1 and the largest possible roundoff error $2^{24}$. The last term on the numerator is the smallest number 1. I'll give you 0.5 point bonus boost.




Yes you are right: in Question A1Q2b and A1Q2d, we are seeking the smallest possible positive number. Thanks for pointing this out. I'll give you 2 points bonus boost.



$\pi$ 