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Gaussian elimination (for square matrices) is O(n^3) arithmetic operations and it's one of the most important algorithms in any scientific domain.



I’ll allow that perhaps I should have said “cubic” instead of “quadratic” - there are much worse orders in the menagerie than n^3. But it’s a constraint we bang into over and over again. We use these systems because they’re cheaper than humans, yes? People are still trying to shave off hundredths of the exponent in matrix multiplication for instance. It makes the front page of HN every time someone makes a “breakthrough”.




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