Questions tagged [accuracy]

Let's say I have two numbers $x$ and $y$ which I'd like to compare to see whether they are equal up to their first $N$ digits. For instance $ 1.002 \approx 1.001$ and $1002 \approx 1001$ up to 3 digits. Intuitively, this means that the difference of…

I have the following expression $$ \frac{a^{(k)}}{k!} $$ where $a^{(k)}$ is the rising factorial. Is it better to evaluate it using floating-point arithmetic separately, that is, call a function that returns the numerator and another function that…

I'm trying to understand the notion of relative error for vectors in $\mathbb{R}^n$, but it's not "clicking" somehow. $$\operatorname{\varepsilon-rel}(x_\text{approx}, x) = \frac{||x_\text{approx} - x ||}{||x||}$$ The intuition I have for the…