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Based on your empirical knowledge.

This paper suggests a nonlinearly accelerated Fourier series approach, such as the one proposed here, but I have one constraint: we should be able to express the method as a linear combination of the function $F$ at different frequencies $s$, that is

$f(t) \approx \sum\limits_{i=1}^N w_i^t \, F(s_i^t)$

In this equation I am looking for the most accurate algorithm that requires the lowest $N$.

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  • $\begingroup$ Is there anything known about $F$ or $f$? Or we are looking at purely arbitrary $F$? $\endgroup$ – Anton Menshov May 22 '18 at 8:11

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