matlab计算误差问题提问

hadd

麻烦问一下，使用matlab进行数值计算时，为什么会出现这样的误差，如何解释？

quantus

这是浮点数的舍入误差很正常的

hadd

   

quantus 发表于 2021-7-10 17:05
这是浮点数的舍入误差很正常的

多问一下，这种误差的精度可以提升吗，通过什么方式呢？

quantus

   

hadd 发表于 2021-7-10 17:14
多问一下，这种误差的精度可以提升吗，通过什么方式呢？

不能提升, 不影响普通的计算, 这是非常常见的问题

osmanali

This a common error to all calculation dealing with double precision IEEE754 representation and not specific to matlab.

As you know the calculation is done internally in binary (base 2) and displayed in base 10. A conversion between base 2 and base 10 is always done. When dealing with fractionnal numbers (>1), the conversion can not be exact and an error will rise. The algorithm has to do a rounding.
In double precision the number of significant digits is 16. So the last digit in your case is incorrect because of the conversion; it is equal to 3 insteed of 0.

I recommand the Following article for further explanation
https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

hadd

   

osmanali 发表于 2021-7-11 02:24
This a common error to all calculation dealing with double precision IEEE754 representation and not  ...

谢谢