A root-finding algorithm is a numerical algorithm for finding a value x such that f(x) = 0, for a given function f.
The bisection method repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing.
Brent's root-finding algorithm combines super-linear convergence with reliability of bisection.
Halley's method is an iterative root finding method for a univariate function with a continuous second derivative, i.e., a C2 function.
The Newton-Raphson method is as follows: one starts with an initial guess which is reasonably close to the true root, then the function is approximated by its tangent line (which can be computed using the tools of calculus), and one computes the x-intercept of this tangent line (which is easily done with elementary algebra).
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