Question-Sum!!

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mathmari
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Question-Sum!!

Postby mathmari » Wed Oct 30, 2013 8:12 pm UTC

Hello :) !! I noticed,by writing a program in c,that,calculating a sum backwards gives a better approximation of the real value of the sum than calculating it forwards..Why does this happen??? :shock: :?:

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Dopefish
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Re: Question-Sum!!

Postby Dopefish » Wed Oct 30, 2013 9:56 pm UTC

What do you mean?

Order of the sum as in "double x = 5.3+4.7;" is giving you a different number than "double x = 4.7+5.3;"?

It might be worthwhile to post an example of the code that's giving odd results.

(Also, I suspect this is gonna end up being more of a coding type question than math, with an answer either being an issue with how numbers are represented under-the-hood or an outright coding error, rather than an unusual aspect of math itself at play.)

alessandro95
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Re: Question-Sum!!

Postby alessandro95 » Wed Oct 30, 2013 10:02 pm UTC

It is probably related to the floating point representation of reals but that should happen only on some particular sums, can you show us exactly which sum(s) are you speaking about?
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Re: Question-Sum!!

Postby elasto » Wed Oct 30, 2013 10:12 pm UTC

If you are trying to add a wide range of fixed-precision numbers together, it's better to start with the small ones and finish with the big: Crudely speaking, adding the small ones together gives them a chance to become big, and so add to the big numbers correctly - whereas starting big and then adding small, the small ones will just get ignored.

See a thread like this for how to add numbers together with perfect precision: http://stackoverflow.com/questions/3941 ... nt-numbers

mathmari
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Re: Question-Sum!!

Postby mathmari » Thu Oct 31, 2013 12:31 am UTC

alessandro95 wrote:It is probably related to the floating point representation of reals but that should happen only on some particular sums, can you show us exactly which sum(s) are you speaking about?


The sum I am referring to is: Σ_{k=1}^{n}{1/k^2}.
Why is the approximation better at the backward sum in this case?

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Re: Question-Sum!!

Postby ahammel » Thu Oct 31, 2013 12:37 am UTC

mathmari wrote:The sum I am referring to is: Σ_{k=1}^{n}{1/k^2}.
Why is the approximation better at the backward sum in this case?
He was probably asking you to post code snippets that give different results when you sum the same numbers in different order.
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elasto
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Re: Question-Sum!!

Postby elasto » Thu Oct 31, 2013 12:46 am UTC

mathmari wrote:The sum I am referring to is: Σ_{k=1}^{n}{1/k^2}.
Why is the approximation better at the backward sum in this case?

Because going backwards adds small numbers before big numbers (see my previous post).

Btw: Two threads, both posted on the same day, both querying why the same series sums differently forwards to backwards? Homework? viewtopic.php?f=17&t=106157#p3487968

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Re: Question-Sum!!

Postby gmalivuk » Thu Oct 31, 2013 2:55 am UTC

Yeah, this looks like it's a question about something brought up in that other thread, which means any further discussion of it can happen in that other thread as well.
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