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Math Help - Interpolation of adjusted square roots...emergency

  1. #1
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    Interpolation of adjusted square roots...emergency

    We've got a project where we're required to interpolate. We've got 10 values, square roots of 10 to 1. These roots are then adjusted by adding 50% to root of 10, 40% to root of 9, 30 % to root of 8, 20% to root of 7 and 10% to root of 6. Then again, 10% to root of 5, 20% to root of 4, 30% to root of 3, 40% to root of 2 and 50% to root of 1.

    It looks like this:
    3.16 + 50%=4.74
    3 + 40%=4.2
    2.83 + 30%=3.68
    2.65 + 20%=3.17
    2.45 + 10%=2.69
    2.24 + 10%=2.46
    2 + 20%=2.4
    1.73 + 30%=2.25
    1.41 + 40%=1.98
    1 + 50%=1.5

    Now we take cumulative totals and the final total is 29.08.
    Now, if 10 is 4.74, 20 is 8.94(sum of 4.74 and 4.2)....90 is 27.58(sum of 1st 9 items or say 29.08-1.5)...

    Can I interpolate and find values of say 3, 27, 67, 83 etc. now that we can values of all multiples of 10?

    I actually tried using Newton's Approximation Formula but it either didn't work all the time or it seems it is giving approximate values which is of little use.
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  2. #2
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    Aug 2010
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    Well its basically this:

    x sqrt(x) %inc y sum z
    --- ------- ---- ---- ----- ----
    10 3.16 50% 4.74 4.74 10
    9 3.00 40% 4.20 8.94 20
    8 2.83 30% 3.68 12.62 30
    7 2.65 20% 3.17 15.79 40
    6 2.45 10% 2.69 18.48 50
    5 2.24 10% 2.46 20.94 60
    4 2.00 20% 2.40 23.34 70
    3 1.73 30% 2.25 25.59 80
    2 1.41 40% 1.98 27.57 90
    1 1.00 50% 1.50 29.07 100

    So now I want to find values of say when z is equal to 3, 25, 47,94 etc. Is Interpolation possible? How? And note you cannot do something like the following which is linear Interpolation which is just not accurate.

    z sum
    --- -----
    20 8.94
    27 ?
    30 12.62

    The approximation would be

    8.94 + (27-20)/(30-20)*(12.62-8.94) = 8.94 + 0.7*3.68 = 11.516

    This is simply 7/10 of the way from 8.95 to 12.62.

    Obviously this is not correct. The value for z=27 would be something more than 11.516.
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