Understanding Precision in Matlab

Question

Ahmad Gad 2020-7-1

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/557545-understanding-precision-in-matlab

评论： Walter Roberson 2020-7-1

I have a simple question. How to split the different between the two numbers into 1e6 increment (unisg linspace)?

The numbers: 5.047639467288342e+4 and 5.047639467288343e+4.

Thanks

2 个评论
显示无隐藏无

Stephen23 2020-7-1

在 MATLAB Online 中打开

"How to split the different between the two numbers into 1e6 increment (unisg linspace)?"

You can't. There are no binary floating point numbers inbetween the two values that you gave.

We can confirm this very easily by noting that their hex representations differ only by 1:

>> A = 5.047639467288342e+4;
>> B = 5.047639467288343e+4;
>> num2hex(A)
ans = 40e8a58ca12906dd
>> num2hex(B)
ans = 40e8a58ca12906de

Ahmad Gad 2020-7-1

Thank you! Then, I have to consider changing the algorithm then.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Walter Roberson 2020-7-1

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/557545-understanding-precision-in-matlab#answer_459346

在 MATLAB Online 中打开

You cannot do that with double precision.

If you have the symbolic toolbox then:

r = linspace(sym('5.047639467288342e+4'), sym('5.047639467288343e+4'), 1e6+1);

Note that the results will be symbolic numbers with higher precision than double(), so if you were to double() them, it would be with loss of precision

2 个评论
显示无隐藏无

Ahmad Gad 2020-7-1

The code is numeric and those values will be inserted a matrix determinant function. I think it will be time consuming.

Walter Roberson 2020-7-1

在 MATLAB Online 中打开

Determinants can have a lot of problems with cancellation. If you were to use symbolic numbers it would be better to use

r = linspace(sym(5.047639467288342e+4,'f'), sym(5.047639467288343e+4,'f'), 1e6+1);

However, symbolic determinants are slow. To put 1e6 numbers into an array you would need an array at least 1e3 x 1e3, and a proper accurate determinent of that would involve over 4 * 10^2567 terms.

请先登录，再进行评论。