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Least squares approximation of a function?

  1. Mar 29, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the least squares approximation of cos^3(x) by a combination of sin(x) and cos(x) over the interval (0, 2pi)

    2. Relevant equations


    3. The attempt at a solution
    I know how to find a least squares approximation with vectors, but I don't even know how to start with a function? The normal equation wouldn't work here because there are no vectors correct? The answer in the back of the book gives sin (x)+(3/4)cos(x), but I don't even know what that answer means. Please help.
     
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  3. Mar 29, 2016 #2

    Simon Bridge

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    You won't be able to do it by folowing a formula... you need to understand what least squares regression is and apply the principle. The formula for vectors should have been derived for you. Note: cos and sin are vectors.

    So if you had an arbitrary vector, ##\vec a## and you needed it in terms of two other vectors ##\vec u## and ##\vec v##... how would you go about it?
     
    Last edited: Mar 29, 2016
  4. Mar 30, 2016 #3

    LCKurtz

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    Perhaps you don't know what the answer means because you don't know the definition of least squares approximations for functions. Surely it is in your text. Or looking here:

    http://homepage.math.uiowa.edu/~atkinson/ftp/ENA_Materials/Overheads/sec_4-7.pdf

    might help you get started. Also, I think your text answer isn't correct.
     
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