What happens when numbers get very small?
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Hi
My computation works with very small physical quantities. I have numbers in the order of 10^-14 which will be multiplied with numbers in about the order of 10^3 to 10^-8. Typing "eps" on the console results in something around 10^-16.
Does Matlab automatically adjust precision to handle these extremely small numbers? Do I have to worry about quantization errors when numbers get small? What about performance issues?
(Basically, I could also change the units of physical constants to bigger values, but I'd like to avoid this.)
Best regards, Michael
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Iain
2014-2-12
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Matlab simply uses standard double format numbers.
This gives you about 15 significant figures of precision from 10^-300 to 10^300 -ish.
When multiplying "a * b" you're likely to get quantisation errors in the order of: eps(a*b), eps(a) * b or eps(b)*a.
You should worry about these quantisations errors when you add large numbers of small values to bigger values (like the obvious way to numerically integrate).
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Andreas Goser
2014-2-12
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In most applications I am aware of, one simply uses scaling like multiplying each datapoint by 1e12 etc. In my experience very small numbers are not a problem per se - only in situations where there very different order of magnitudes in ONE matrix or there are operation with data with very different order of magnitudes.
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