Estimate the absolute error

Asked Feb 04 '20 at 17:32

Active Feb 04 '20 at 18:13

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Assume that we know the approximate value a* of the real number a, and the approximate value b* of the real number b, i.e. a≈a* and b≈b*. Assuming that a, b ∈ [−2, 4], estimate the absolute error abserr(a · b, a* · b*).

Can someone help me with this question?

There is a hint that I can use |ab - a* b*| = |ab - ab* + ab* - a* b*| and that x* 10^-k < x < x* + 10^-k

edited Feb 04 '20 at 18:13

asked Feb 04 '20 at 17:32

You mean $|ab - a b^* + ab^* - a^* b^*|$. – Robert Israel Feb 04 '20 at 17:34
Right my mistake – Feb 04 '20 at 17:35
Further hint: by triangle inequality this $\le |a b - a b^| + |ab^ - a^* b^*|$. – Robert Israel Feb 04 '20 at 17:36
This is an obvious thing not a hint. – Feb 04 '20 at 18:00
The whole thing is not much less obvious. – Robert Israel Feb 04 '20 at 18:25

Estimate the absolute error

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