A spiking neural network (SNN) is defined that includes artificial neurons interconnected by artificial synapses, the SNN defined to correspond to one or more numerical matrices in an equation such that weight values of the synapses correspond to values in the numerical matrices. An input vector is provided to the SNN to correspond to a numerical vector in the equation. A steady state spiking rate is determined for at least a portion of the neurons in the SNN and an approximate result of a matrix inverse problem corresponding to the equation is determined based on values of the steady state spiking rates.