# Uniform approximation

1. Apr 8, 2008

### Tolya

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

Thanks for any ideas!!

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