Methodological study demonstrates guaranteed superlinear convergence in one-dimensional root finding, highlighting improved computational speed over standard bisection.
An algorithm is presented for finding a zero of a function which changes sign in a given interval. The algorithm combines linear interpolation and inverse quadratic interpolation with bisection. Convergence is usually superlinear, and is never much slower than for bisection. ALGOL 60 procedures are given.
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Richard P. Brent (1971) studied this question.
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