Section 2.1 of Burden and Faires: Bisection

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Convergence of Bisection

Theorem 2.1 Suppose that and . The bisection method generates a sequence approximating a root of with

,

when .

So, using the terminology of section 1.3, we'd say that the sequence converges to as with constant .

In the big picture, this means that we get one additional digit of binary accuracy with each iteration of bisection.