Results 1 to 4 of 4

Math Help - least square approximations

  1. #1
    Junior Member
    Joined
    Dec 2011
    Posts
    57
    Thanks
    1

    least square approximations

    Let t_{j}=j/100, a_{j}=j,b_{j}=-j for j=0,...,99. Determine the values of c_{l},d_{m} for l=0,...,5,m=1,...,4, so that
    P(t)=c_{0}+\sum_{k=1}^{4}(c_{k}\textup{cos}(2\pi{k  t})+d_{k}\textup{sin}(2\pi{kt}))+c_{5}\textup{cos}  (10\pi{t})
    is the least squares approximation to the data points (t_j,x_j) for j=0,...,99.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: least square approximations

    Quote Originally Posted by alphabeta89 View Post
    Let t_{j}=j/100, a_{j}=j,b_{j}=-j for j=0,...,99. Determine the values of c_{l},d_{m} for l=0,...,5,m=1,...,4, so that
    P(t)=c_{0}+\sum_{k=1}^{4}(c_{k}\textup{cos}(2\pi{k  t})+d_{k}\textup{sin}(2\pi{kt}))+c_{5}\textup{cos}  (10\pi{t})
    is the least squares approximation to the data points (t_j,x_j) for j=0,...,99.
    More context would help with this, like is the data known and you want the actual coefficients, or do you want something like the regression equations?

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2011
    Posts
    57
    Thanks
    1

    Re: least square approximations

    Quote Originally Posted by CaptainBlack View Post
    More context would help with this, like is the data known and you want the actual coefficients, or do you want something like the regression equations?

    CB
    Sorry! I realised I left out some details!

    Let t_{j}=j/100, a_{j}=j,b_{j}=-j for j=0,...,99. Define
    f(t)= \sum_{k=0}^{99}(a_{k}\textup{cos}(2\pi{kt})+b_{k}{  sin}(2\pi{kt}))
    .
    Define f(t_{j}) by x_{j} for j=0,...,99.Determine the values of c_{l},d_{m} for l=0,...,5,m=1,...,4, so that
    P(t)=c_{0}+\sum_{k=1}^{4}(c_{k}\textup{cos}(2\pi{k  t})+d_{k}\textup{sin}(2\pi{kt}))+c_{5}\textup{cos}  (10\pi{t})
    is the least squares approximation to the data points (t_j,x_j) for j=0,...,99.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: least square approximations

    Quote Originally Posted by alphabeta89 View Post
    Sorry! I realised I left out some details!

    Let t_{j}=j/100, a_{j}=j,b_{j}=-j for j=0,...,99. Define
    f(t)= \sum_{k=0}^{99}(a_{k}\textup{cos}(2\pi{kt})+b_{k}{  sin}(2\pi{kt}))
    .
    Define f(t_{j}) by x_{j} for j=0,...,99.Determine the values of c_{l},d_{m} for l=0,...,5,m=1,...,4, so that
    P(t)=c_{0}+\sum_{k=1}^{4}(c_{k}\textup{cos}(2\pi{k  t})+d_{k}\textup{sin}(2\pi{kt}))+c_{5}\textup{cos}  (10\pi{t})
    is the least squares approximation to the data points (t_j,x_j) for j=0,...,99.
    This is now a numerical problem, consider using the Excel solver to find the best fit.

    (Fourier theory suggests that c_0\approx 0 and c_i\approx 100 for i=1..5 and d_i\approx 100 for i=1 .. 4 )

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Polynomial L^2 approximations
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 13th 2010, 11:28 PM
  2. ti-84 approximations
    Posted in the Calculators Forum
    Replies: 1
    Last Post: December 3rd 2009, 08:29 PM
  3. First Degree Approximations
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 16th 2009, 06:25 PM
  4. Approximations, help wit 1 more please
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 18th 2007, 03:43 PM
  5. What are Linear approximations used for
    Posted in the Calculus Forum
    Replies: 16
    Last Post: October 17th 2006, 04:31 PM

Search Tags


/mathhelpforum @mathhelpforum