![]() In particular, you do not need any special information about the function \(f\) except the ability to evaluate it at various points in the interval. The bisection algorithm is useful, conceptually simple, and is easy to implement. Using this information, we can present the bisection algorithm. So if \(f(a) < \gamma < f(b)\), then there exists a \(c\in\) such that \(f(c)=\gamma\). The theoretical underpinning of the algorithm is the intermediate value theorem which states that if a continuous function \(f\) takes values \(f(a)\) and \(f(b)\) at the end points of the interval \(\), then \(f\) must take all values between \(f(a)\) and \(f(b)\) somewhere in the interval. The algorithm starts with a large interval, known to contain \(x_0\), and then successively reduces the size of the interval until it brackets the root. The goal is to find a root \(x_0\in\) such that \(f(x_0)=0\). The bisection algorithm is a simple method for finding the roots of one-dimensional functions.
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December 2022
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