Post Closed as "not a real question" by Igor Rivin, S. Sra, Gerald Edgar, Bruce Westbury, Will Jagy
3 added 6 characters in body

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:

1. For large numerical vectors x, instead of computing x^2, compute x*x. This speeds up calculations for reasons...(?)
2. 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 one something quicker and dirtier

2 added 176 characters in body

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:

1. For large numerical vectors x, instead of computing x^2, compute x*x. This speeds up calculations for reasons...(?)
2. 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 one quicker and dirtier

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