a-hackers-guide-to-numerical-analysis

[bollu]

a-hackers-guide-to-numerical-analysis

[ziofil]

1. absolute errror <--- typing error ^^

[crdrost]

It is not transparent to me why this definition is sensible.

Exponentials and logarithms are inverses of each other, so the "significant figures" calculation is, roughly, the base-10 logarithm of the relative error, from which the relative error can be calculated. "I know it to 5 significant figures" is roughly "I know it to one part in 10⁵." It's a crude way of speaking. A half-significant-figure is a factor of roughly 3 because 3² is nine which is roughly 10, to get slightly more granular ("two and a half orders of magnitude" = a factor of 300ish).

Note that the rules are somewhat subtle involving actual manipulations, indeed there are these problems with catastrophic cancellation etc.

[ziofil]

That reminds me, there exist tools to automatically (within limits) find the most accurate version of a computation: https://herbie.uwplse.org

[jmbr]

Nice collection of topics!

Suggestion: mention the expm1 function when discussing $e^x - 1$

[falematte]

Are you using org-babel to execute C blocks?