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preciseness of the calculation

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bahare
bahare 2011-11-18
关闭: MATLAB Answer Bot 2021-8-20
Hi I have two rows of data, consists of 3 numbers in each row. which are for example a,b and c. a and c are constant in each row, but b is changed. I sum the numbers in each row, however the answers are the same even though b is different. here is the numbers: a= 9237639,3400267 b=184,279078050855 c=23,3803295791066 a+b+c= 19237846,9994343 a=19237639,3400267 b=184,279078052863 c=23,3803295791066 a+b+c= 19237846,9994343
why these two summations are different?

回答(1 个)

Jan
Jan 2011-11-18
This is an effect of the limit internal precision. DOUBLEs are represented by 64 bits such that the mantissa has a precision of 53 bits. This is about 16 digits. If you add numbers of different size, small differences can dissappear. See:
a = 1.0E17 + 1 - 1.0E17
% >> 0
although 1 would be mathematically correct. But the intermediate result of the first two summands cannot be represented accurately.
Using the standard IEEE arithmetics, there must be a difference between "mathematically" and "numerically". See also: eps and FAQ 6.1.
BTW. Reading the FAQ completely is always a good idea.

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