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在数学的历史上,算法的发展是数学发展的一种重要进程.一切有次序的形式运算归根结底都是一种算法,特别地,字母运算本身就是一种算法.中学数学教材引进了算法的学习,让学生知道了求一个一元方程近似解的“二分法”、求两个正整数的最大公约数的“辗转相除法”等经典算法案例.那么,隐藏在这些具体算法中的,或者说引导这些算法产生的策略是什么呢?本文探讨一下这个问题。归纳起来就是三种策略:逐步递归、无限逼近和随机模拟.
In the history of mathematics, the development of algorithms is an important process of mathematical development.All the formal forms of operation in the final analysis are an algorithm, in particular, the alphabet operation itself is an algorithm.Mathematics textbooks introduced the learning algorithm , Let the students know the classical algorithm of seeking the “dichotomy” of the approximate solution of a univariate equation, and dividing the greatest common divisor of two positive integers, etc. Then, hidden in these concrete algorithms , Or what are the strategies that guide these algorithms? This article explores this issue. Summarized are three strategies: gradual recursion, infinite approximation and stochastic simulation.