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Math Help - Analysis Question

  1. #1
    Junior Member
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    Analysis Question

    Hi all,

    I have a timeseries data set that converges to the exact (attached). I would like to have some sort of tolerance in my programs but would like to do it numerically. It would be something like min(max(distance_from_exact_of_timeseries)). It is difficult to explain but I hope the picture will help. If I fit a linear regression line to the data I get something along the lines of what I am looking for but I can only do this with the tools after the program has run which defies the point.
    Attached Thumbnails Attached Thumbnails Analysis Question-rho_u_convrgence_plot.pdf  
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  2. #2
    A Plied Mathematician
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    So, what is your question? Are you wanting to be able to approximate the exact solution in real-time, and not wait to post-process?
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  3. #3
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    I apologise it's probably unclear. I would like a bound. As the approximate solution oscillates closer to the exact solution I would like to input a value say 0.01. When the approximate solution gets to the point where it is oscillating at 0.01 intervals about the exact solution it stops. So I know my approximate solution is within 0.01 error of the exact.

    This would be easy if it was linear because it would just be

    while abs(approx-exact)>0.01
    continue program
    end

    however in my case the approximate solution passes through the exact solution and this statement doesn't work.

    Is there a way to statistically or otherwise determine the minimum maximum value

    Thank you for your reply
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  4. #4
    A Plied Mathematician
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    Hmm. I would probably run a peak-finding routine: as soon as the peaks are less than your tolerance away from the exact value, stop.
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