MATLAB: The most close approximation to zero

approximationdigitserrors

Hello, I want to ask you about the number of smaller approximation close to zero that matlab can understands. I mean I have a function and I wrote that If abs(….)<1e-15 (I want it =0 but because of small errors it has to be very very close to zero.) .. end
but when the number is close to this and has to read the loop it doesnt, so the function goes wrong. And also there many errors. Do you know if I can have a number closer to zero? (I wrote e-15 because I know that matlab gives till 15 digits after '.' when you have format long)

Best Answer

Hi,
there are some aspects to this question. The smallest number you can represent is much smaller:
realmin
ans =
2.2251e-308
But this is not what you are looking for. The accuracy is more what you are looking for:
eps
ans =
 2.2204e-16
But keep in mind that the tolerance usually should be a relative tolerance, not an absolute one (difference of 10 degrees on earth makes much more of a difference than 10 degrees on the surface of the sun). So I would suggest to use something like
xExact = 42.0;
xIteration = 41.9;
while abs(xExact-xIteration) < 100*eps(xExact)
This way you have a relative error test. Note, the 100 is arbitrary and depends heavily on what you are really doing.
Titus
Related Question