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Approximating polynomials

  1. Mar 31, 2007 #1
    1. The problem statement, all variables and given/known data
    find closest function a+bx3 to x2 on the iterval [-1,1]
    (we consider standard inner product (f,g) = integral(-1 to 1):fgdx

    So, here is my attempt, but I got a suspicious result:

    [(1,1) (1,x3)] [a]
    [(1,x3) (x3,x3)]
    =
    [(1,x2)]
    [x3, x2)]

    then after I've done all the integration I came up with this:
    [2 0] [a]
    [0 2/7]
    =
    [1/3]
    [0]
    which means that x3 term disappears....:frown:
     
  2. jcsd
  3. Mar 31, 2007 #2

    Dick

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    Homework Helper

    I can't help you fix it. Because you are completely correct. Why do you think that is suspicious? Find ways to check yourself.
     
  4. Mar 31, 2007 #3

    Dick

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    Science Advisor
    Homework Helper

    You are approximating an even function over a symmetric interval. Can adding part of an odd function help you?
     
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