Does there exist a simple, cheatsheet-like document which compiles the best practices for mathematical computing? If not, could someone respond with a list of the top best practices? E.g., it would include items like:

- For large numerical vectors
`x`

, instead of computing`x^2`

, compute`x*x`

. This speeds up calculations for reasons...(?) - To solve a system $Ax = b$, never solve $A^{-1}$ and left-multiply $b$. Lower order algorithms exist (e.g., Gaussian elimination)

BACKGROUND: I'm finding papers where programmatic implementations are quite different from what derived analytic expressions would suggest. Different factorings, expansions, and approximations are used all over the place. I don't think it's simply arbitrary. But the problem is that I have no sense of WHY they're doing what they're doing. I think a cheatsheet-like document would help with this.

UDPATE: I did find a nice numerical analysis cheatsheet here. But I'm looking for something quicker and dirtier

`There is no royal road to learning, sire' and he said to me`

Bloody well build one or I shall have your legs chopped off. Use as many slaves as you like.' A refreshingly direct approach, I always thought. Not a man to mince words. People, yes. But not words." $\endgroup$ – Will Jagy Sep 21 '11 at 20:45