“bisection method”的概念、定义、习题解题方法及翻译-数学辞典

单词

bisection method

释义

bisection method

A numerical method for finding a root of an equation f(x) = 0. If values a and b are found such that f(a) and f(b) have opposite signs and f is continuous on the interval [a, b], then (by the intermediate value theorem) the equation has a root in (a, b). The method is to bisect the interval and replace it by either one half or the other, thereby closing in on the root.

Let $inline$ . Calculate f(c). If f(c) has the same sign as f(a), then take c as a new value for a; if not (so that f(c) has the same sign as f(b)), take c as a new value for b. (If it should happen that f(c) = 0, then c is already a root.) Repeat this whole process until the length of the interval [a, b] is less than 2ε, where ε is the desired accuracy, specified in advance. The midpoint of the interval can then be taken as an approximation to the root, and the error will be less than ε. Compare binary search algorithm.

http://archives.math.utk.edu/visual.calculus/1/bisection.3/index.html

• An interactive page which demonstrates the method for finding a root of a cubic equation.

随便看

数学辞典收录了4151条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。