A spiking neural network (SNN) is implemented on a neuromorphic computers and includes a plurality of neurons, a first set of the plurality of synapses defining feed-forward connections from a first subset of the neurons to a second subset of the neurons, a second subset of the plurality of synapses to define recurrent connections between the second subset of neurons, and a third subset of the plurality of synapses to define feedback connections from the second subset of neurons to the first subset of neurons. A set of input vectors are provided to iteratively modify weight values of the plurality of synapses. Each iteration involves selectively enabling and disabling the third subset of synapses with a different one of the input vectors applied to the SNN. The weight values are iteratively adjusted to derive a solution to an equation comprising an unknown matrix variable and an unknown vector variable.