most recent 30 from http://mathoverflow.net 2013-05-22T02:28:22Z http://mathoverflow.net/feeds/question/76067 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/76067/mathematical-computing-rules-of-thumb brianjd 2011-09-21T15:24:58Z 2011-09-21T16:16:18Z

<p>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:</p> <ol> <li>For large numerical vectors <code>x</code>, instead of computing <code>x^2</code>, compute <code>x*x</code>. This speeds up calculations for reasons...(?)</li> <li>To solve a system $Ax = b$, never solve $A^{-1}$ and left-multiply $b$. Lower order algorithms exist (e.g., Gaussian elimination)</li> </ol> <p>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. </p> <p>UDPATE: I did find a nice numerical analysis cheatsheet <a href="http://www.tfinley.net/notes/cs421-cheat-sheet4.pdf" rel="nofollow">here</a>. But I'm looking for something quicker and dirtier</p>