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Homework Help: Uniform approximation

  1. Apr 8, 2008 #1
    Function [tex]f(t)[/tex] specified on [tex][t_0;t_1][/tex] has a necessary number of derivatives. Find algorithm which can build uniform approximations of this function with help of partial sums:
    [tex]\sum_{i=1}^{N}\alpha_i e^{-\beta_i t}[/tex].
    That is, find such [tex]\alpha_i[/tex], [tex]Re(\beta_i)\geq 0[/tex] satisfying the expression:
    [tex]\min_{\alpha_i, ~\beta_i}\left( \max_{t\in [t_0;t_1]} \left| f(t)-\sum_{i=1}^{N}\alpha_i e^{-\beta_i t}\right| \right)[/tex]
    Also consider a function specified on [tex][t_0;+\infty)[/tex]

    Thanks for any ideas!!
  2. jcsd
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