Introduction to Mathematical Biology by Ching Shan Chou & Avner Friedman

Author:Ching Shan Chou & Avner Friedman
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

7.1.2 Bisection Method

The idea of the bisection method comes from the intermediate value theorem: continuous function f must have at least one root in the interval (a, b) if f(a) and f(b) have opposite signs. The method repeatedly bisects an interval then selects a subinterval in which a root must lie (the function values at the two ends of the subinterval have opposite signs). Suppose that we have two initial points a 0 = a and b 0 = b such that f(a)f(b) < 0. The method divides the interval into two by computing the midpoint of the interval. If c is a root, that is f(c) = 0, then the algorithm terminates. Otherwise, the algorithm checks f(a)f(c) and f(c)f(b), one of which must be negative. If f(a)f(c) < 0, the root must lie in the interval (a, c) and the method sets a as a 1 and c as b 1. If f(c)f(b) < 0, the root must lie in the interval (c, b) and the method sets c as a 1 and b as b 1. Repeating this process, we can construct a sequence of intervals [a n , b n ] such that

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