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relative error for A

evinda

Well-known member
MHB Site Helper
Apr 13, 2013
3,720
Hey!!! :rolleyes: I have also an other question :eek:
Suppose the base $\beta =10$ ,the precision $t=3$, $-L=U=10$ and $$A=(317+0.3)-(171.499+145.501)$$
I have to find the relative error for $A$.
We don't make rounding.For example,if we have the value $345.924$ it is equal to $0.345924*10^3$ and the corresponding floating number is $0.345*10^3$.
I found that it is equal to
$$\frac{||A-fl(A)||}{||A||}=\frac{7}{5}=2.33$$
Could you tell me if it is right?
 

evinda

Well-known member
MHB Site Helper
Apr 13, 2013
3,720
Hey!!! :rolleyes: I have also an other question :eek:
Suppose the base $\beta =10$ ,the precision $t=3$, $-L=U=10$ and $$A=(317+0.3)-(171.499+145.501)$$
I have to find the relative error for $A$.
We don't make rounding.For example,if we have the value $345.924$ it is equal to $0.345924*10^3$ and the corresponding floating number is $0.345*10^3$.
I found that it is equal to
$$\frac{||A-fl(A)||}{||A||}=\frac{7}{5}=2.33$$
Could you tell me if it is right?
I found that A=0.3 and fl(A)=1..
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,780
I found that A=0.3 and fl(A)=1..
Looks good!! ;)


... but doesn't that mean that:
$$\frac{||A-fl(A)||}{||A||} = \frac{|0.3 - 1|}{|0.3|} = \frac{0.7}{0.3} = 2.33$$

Oh wait! You also got $2.33$... while you shouldn't have. :eek: :rolleyes:
 

evinda

Well-known member
MHB Site Helper
Apr 13, 2013
3,720
Looks good!! ;)


... but doesn't that mean that:
$$\frac{||A-fl(A)||}{||A||} = \frac{|0.3 - 1|}{|0.3|} = \frac{0.7}{0.3} = 2.33$$

Oh wait! You also got $2.33$... while you shouldn't have. :eek: :rolleyes:
I accidentally wrote $\frac{7}{5}$ :eek: I meant that it is equal to $\frac{7}{3}$..

Thank you very much!!!!! (Mmm)