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C3 coursework.....error bounds??

Discussion in 'Mathematics' started by bonusfeature, Nov 25, 2007.

  1. Hello, I am doing this coursework and I am a little bit unsure about how to state my error for decimal search.

    I have established that the root lies between -2.28682 and -2.28683.

    Do I say that the solution is -2.2868 +/- 0.00005, since that was the root from my previous search that I have now established it is closer to?

    Or can I say that it is -0.286825 +/- 0.000005, as this will cover all values in my range?

    Thanks in advance for any help, BF.
     
  2. Hello, I am doing this coursework and I am a little bit unsure about how to state my error for decimal search.

    I have established that the root lies between -2.28682 and -2.28683.

    Do I say that the solution is -2.2868 +/- 0.00005, since that was the root from my previous search that I have now established it is closer to?

    Or can I say that it is -0.286825 +/- 0.000005, as this will cover all values in my range?

    Thanks in advance for any help, BF.
     
  3. Thanks for that Calum. Can anyone tell me why it isn't -0.286825 +/- 0.000005? Surely that covers all the possible values in my range?
     
  4. We allow our students to use either.

    In fact, in your case I would say it's more sensible if you're doing the change of sign method to say it's -2.286825 +/- 0.000005 because the method gives you an interval at the end.

    However, for Newton-Raphson and rearrangement (i.e. the fixed point methods) they tend to converge on an actual value - so for these give them to a certain number of decimal places e.g. 1.05142 to 5dp WARNING: I think you have to give these to at least 5sf but check the coursework guide.

    NOTE: for the fixed point iterations you must check your result by trying e.g. for the above result:

    f(1.051415)
    f(1.051425)

    One should be positive and one negative, thus confirming your result to the number of decimal places given.

    Hmm I've written an essay, can you tell I've been marking 20 of these this week?
     
  5. Thanks for that debecca. Feel a bit more confident of my answers now.
     

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