Abstract <p>A fast numerical method is proposed for the problem of reconstructing the source function in the Smoluchowski coagulation–fragmentation equation. The method is based on an earlier work, but a more detailed description is presented for the transition from the coagulation–fragmentation equation to the final system of variational equations and an iterative process. Low-rank matrix algorithms are introduced into this process to reduce the computational complexity at each iteration. Due to this technique, the computations are accelerated by thousands of times without losing the accuracy of the original algorithm.</p>