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Algorithms to approximate numerically a root of a nonlinear equation or system: for instance, Newton's method, secant method, bisection, etc.
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how to efficiently find level sets (using a modification of a root-finding algorithm)?
I'm trying to find a set of points $\{ a_i | f(a_i) = c_i \}_{i=1}^k$ where $f$ and $\{ c_i \}_{i=1}^k$ are given in sorted order. All $c_i > 0$, $f$ is continuous and monotonically increasing, $f(0) …