mit 计算机科学及编程导论（5）

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文章标签：

#编程 #numbers #python #function #class #算法

本文探讨了在Python中使用浮点数时的常见误解与问题，包括计算机内浮点数表示的局限性、操作导致的误差累积、打印函数的数值舍入以及在比较浮点数时的正确做法。同时强调了培养学生像计算机科学家一样思考的重要性，通过实例展示了改进浮点数计算方法以提高精度与效率的方法。

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words:

confession , auditorium , crunch , mirror , budget deficit , considerably , exponentiation , exponent , obnoxious , mantissa , purist , significand , stroll , hence , decimal , pesky , fraction , etc==etcetera , approximation , implication , accumulate , drive-home , epsilon , successive , spin , bi-section , logarithm , thoroughly , terminology , predicate , fussy , exceed , creep , infamous , constant , equivalent , enormous

notes:

two major parts today : numbers (especially floating point) in python & solve problems involved floating point with computer

一、numbers in python

1、some numbers represented in computer is contrary to your intuition suggests

2、when manipulate floating point , error will grow bigger while the iterating

3、print function prints rounding numbers , so what it prints is not what it is represented in computer

4、worry about "==" on floats : never test the equivalent of floats but how close they are

二、solve problems involved floating point with computer

1、real numbers can't enumerate exhaustively , so we just can guess , check & improve

2、how to improve : successive approximation (in this class professor uses bi-section)

3、what matters the improvement : the speed of the convergence

4、good habits in writing function : check the arguments & give it a limit bound to the iteration

ps:

1、整个课程就是要培养学生像computer scientists般的思考，所以会覆盖很多用计算机解决问题的方法的讲解。这一次就是讲解如何解决涉及浮点数的问题。当涉及浮点数时要注意计算机内的表示只是约数，所以不能得到精确的值，也就是得到的只是符合某种精度的约数值。而如何利用最快、最省资源的算法去求出约数就是关键