# What is the inverse Laplace transform algorithm that is most accurate given the fewest frequencies considered?

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