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1

This is a bit late for you, perhaps, but it might be worth looking at cylindrical algebraic decomposition. CAD takes a general statement in the real closed fields (i.e. an arbitrary boolean statement involving equalities and inequalities), and returns a finite set of "solutions", each of which is a "procedure" to find those solutions by assigning the unknown ...


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$O(n \log n)$ is a polynomial speedup over $O(n^2)$, in particular almost a quadratic speedup. $O(n \log n)$ is big-O of $O(n^k$) for all $k > 1$. Its runtime is therefore between linear and any powerfunction whose exponent is strictly greater than 1. Let $f(n)=n \log n$. Raise it to a power of some value slightly less than 2 to approximate the original ...


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