Error caused by that small difference between two number is divided by a very small number

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Benson Gou
Benson Gou el 30 de Jul. de 2018
Comentada: Walter Roberson el 30 de Jul. de 2018
We have a situation that the difference between two complex numbers is divided by a very small complex number. For example, the complex number is Z=10E-6 + i10E-6. The difference Delta between two complex numbers is about 10E-5. However, because of the noise in these two complex numbers (noise is around 10E-3, but we do not know their specific values). So when we solve S from the equation S = Delta / Z, we got a very big S, which expanded the noise by 10E+3.
Do you know how to obtain a reasonable S (or approximate S) from the above equation?
Thanks a lot!
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Walter Roberson
Walter Roberson el 30 de Jul. de 2018
What would your code expect if the two values were identical? What if they were identical to within round off error?

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