Error on summation of three numbers
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Hi, When we used this commands on commands windows of Matlab 2013a, we found a problem and we couldn't understand why that happened.
>> a=4.2; b=0.8; c=5;
>> a+b-c
ans = 0
>> a-c+b
ans = 2.2204e-16
>> b-c+a
ans = 0
The question is why on the second step (a-c+b) Matlab reached a number except zero! and how we can be sure that doesn't happen anymore?!
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A Jenkins
2014-3-5
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Roger Stafford
2014-3-5
1 个投票
To give you a very brief answer, your computer is using a binary representation of floating point numbers and cannot therefore exactly represent 4.2 and .8 . The resulting round-off errors produce the tiny difference you see here. In other words, round-off errors are causing the addition operation to not be strictly associative. It's the same difficulty a decimal calculator would have adding fractions like 1/3, 1/7, etc. It cannot represent them exactly and therefore makes tiny errors with them.
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