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Solving for a factor in a large sum

  1. Dec 21, 2013 #1
    Dear everyone.

    First of all Merry Xmas, when everybody gets to that.

    I have a problem solving for a factor within a sum.

    My formula looks as follows:

    T = Æ© It * A0t

    The sum runs from t=1 to N, and the aim is to solve for A0, but all my calculations end up extremely messy.

    All the best,

    Dan
     
  2. jcsd
  3. Dec 21, 2013 #2
    What is It?
     
  4. Dec 21, 2013 #3
    Thanks for the reponse.

    That is the t'th observation of I. They have no well-defined relation to t. In other words; just a bunch of numbers.
     
  5. Dec 21, 2013 #4
    In that case, your equation seems to be a general polynomial of order N. I guess N is probably fairly large (as in... not 2 or 3). You will need to use some numerical method to find roots of the function f(A0) = Æ© It * A0t - T.

    I suggest Newton's method, it should be convenient to implement, because you can easily compute the derivative of the function analytically.
     
  6. Dec 21, 2013 #5
    Actually it is not that large (N, that is), it is just that it varies a lot from case to case and hence I have written it as a sum.

    Thanks so much for the response. I will try to see if it gets me any further!
     
  7. Dec 21, 2013 #6
    And just to be clear. The A_0 has t as their exponent. It is not a subscript!
     
  8. Dec 21, 2013 #7
    If N is equal to 3 or 4, the polynomial is still solvable by analytic methods, but in general it is easier to use a numerical technique like Newton's Method (which is very easy to program if you choose to do that).

    The N = 3 case isn't this bad, but consider the solutions for N = 4:

    http://upload.wikimedia.org/wikipedia/commons/9/99/Quartic_Formula.svg

    Of course, if you know ##a## is a solution to the polynomial, you can long divide by ##(x-a)## to reduce the degree by 1.
     
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