稳定性(数值分析) [英] Stability (Numerical analysis)

问题描述

我试图找到满足以下方程式的最大机器编号x:x + a = a，其中a是给定的整数. (我不允许使用eps.)

I'm trying to find the max machine number x that satisfies the following equation: x+a=a, where a is a given integer. (I'm not allowed to use eps.)

这是我的代码(实际上不起作用):

Here's my code (which is not really working):

function [] = Largest_x()

a=2184;
x=0.0000000001
while (x+a)~=a
    x=2*x;
end
fprintf('The biggest value of x in order that x+a=a \n (where a is equal to %g) is : %g \n',a,x);
end

任何帮助将不胜感激.

推荐答案

答案是eps(a)/2.

eps是下一个浮点数的差，因此，如果对浮点数加一半或更少，则不会改变.例如:

eps is the difference to the next floating point number, so if you add half or less than that to a float, it won't change. For example:

100+eps(100)/2==100
ans =
     1

%# divide by less than two
100+eps(100)/1.9==100
ans =
     0

%# what is that number x?
eps(100)/2
ans =
   7.1054e-15

如果您不想依赖eps，则可以将数字计算为

If you don't want to rely on eps, you can calculate the number as

2^(-53+floor(log2(a)))

这篇关于稳定性(数值分析)的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！