The method is applicable for numerically solving the equation f( x) = 0 for the real variable x, where f is a continuous function defined on an interval and where f( a) and f( b) have opposite signs. 2 Example: Finding the root of a polynomial.They allow extending bisection method into efficient algorithms for finding all real roots of a polynomial see Real-root isolation. įor polynomials, more elaborated methods exist for testing the existence of a root in an interval ( Descartes' rule of signs, Sturm's theorem, Budan's theorem). The method is also called the interval halving method, the binary search method, or the dichotomy method. Because of this, it is often used to obtain a rough approximation to a solution which is then used as a starting point for more rapidly converging methods. It is a very simple and robust method, but it is also relatively slow. The method consists of repeatedly bisecting the interval defined by these values and then selecting the subinterval in which the function changes sign, and therefore must contain a root. In mathematics, the bisection method is a root-finding method that applies to any continuous functions for which one knows two values with opposite signs. The bigger red dot is the root of the function. A few steps of the bisection method applied over the starting range.
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