Halving The Interval
This feature is not available right now. In the following homework questions you will discover how interval halving can be used to efficiently find integer roots.
Its efficiency comes from the property that at each step we eliminate half of the interval of possible solutions.
Halving the interval. Thanks for contributing an answer to mathematics stack exchange. Asking for help clarification or responding to other answers. Please try again later. This algorithm is an example of an interval halving or binary search strategy. The method is also called the interval halving method the binary search method or the dichotomy method. Please be sure to answer the questionprovide details and share your research. For polynomials more elaborated methods exist for testing the existence of a root in an interval descartes rule of signs sturms theorem budans theorem. Interval halving is very useful in that it only requires the function to be continuousmore efficient methods like newtons method require that the function is differentiable and that we have to have a good starting point. Interval halving has linear convergence while newtons method has quadratic convergence.
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