Approximate matrix inverse by Fourier approach

172 Views Asked by At

Given a hermititan matrix $A$ with the possibility to generate $e^{-iAt}$ for $t\geq 0$ how would I proceed to approxiamte:

$A^{-1}\approx\sum_j\alpha_je^{-iAt_j}$ $\quad$ with $\alpha_j\in\mathbb{C}$

How could I determine $\alpha_j$ and $t_j$