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MEI C3 coursework - iteration methods, how do I know when I've found the root?

It's hard to explain what exactly I'm asking.

Okay, so you iterate. The value you get from each iteration is different. First it changes by like .x each time, then .0x, then .00x - the difference between iterations gets smaller.

So, say I have two consecutive iterations that are like:

X1 = 1.23456708
X2 = 1.23456196

The first 6 sf are the same, but the numbers are still changing. So can I give the value of the root as 1.2345 accurate to 5 s.f., or do I need to keep iterating until it stops changing?
Accurate to 5 s.f


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Avatar for rxns_00
rxns_00
15
Original post by JordanL_
It's hard to explain what exactly I'm asking.

Okay, so you iterate. The value you get from each iteration is different. First it changes by like .x each time, then .0x, then .00x - the difference between iterations gets smaller.

So, say I have two consecutive iterations that are like:

X1 = 1.23456708
X2 = 1.23456196

The first 6 sf are the same, but the numbers are still changing. So can I give the value of the root as 1.2345 accurate to 5 s.f., or do I need to keep iterating until it stops changing?


The question should specify the accuracy you should provide the answer to?
Original post by drandy76
Accurate to 5 s.f


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Original post by RonnieRJ
The question should specify the accuracy you should provide the answer to?


Sorry, I know that I need the answer accurate to 5 s.f. I'm just not sure if it'd be accurate to 5 s.f. in the example I gave.
Reply 4
Avatar for rxns_00
rxns_00
15
Original post by JordanL_
Sorry, I know that I need the answer accurate to 5 s.f. I'm just not sure if it'd be accurate to 5 s.f. in the example I gave.


Oh I see

If two successive iterations round to the same approximation to 5sf then you're done :smile:

So these two successive iterations both round up to 1.2346 to 5sf so that's the answer you give
Reply 5
Avatar for Zacken
Zacken
22
Original post by JordanL_

The first 6 sf are the same, but the numbers are still changing. So can I give the value of the root as 1.2345 accurate to 5 s.f., or do I need to keep iterating until it stops changing?


You can give it, the first 6 s.f are the same, hence you can give the first 5 s.f as the root.
Got it, thanks for the help!

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