  Resonator networks are ubiquitous in natural and engineered systems, such as
solid-state materials, neural tissue, and electrical circuits. To understand
and manipulate these networks, it is essential to characterize their building
blocks, which include the mechanical analogs of mass, elasticity, damping, and
coupling of each resonator element. While these mechanical parameters are
typically obtained from response spectra using least-squares fitting, this
approach requires a priori knowledge of all parameters and is susceptible to
large error due to convergence to local minima. Here we validate an alternative
algebraic means to characterize resonator networks with no or minimal a priori
knowledge. Our approach recasts the equations of motion of the network into a
linear homogeneous algebraic equation and solves the equation with a set of
discrete measured network response vectors. For validation, we employ our
approach on noisy simulated data from a single resonator and a coupled
resonator pair, and we characterize the accuracy of the recovered parameters
using high-dimension factorial simulations. Generally, we find that the error
is inversely proportional to the signal-to-noise ratio, that measurements at
two frequencies are sufficient to recover all parameters, and that sampling
near the resonant peaks is optimal. Our simple, powerful tool will enable
future efforts to ascertain network properties and control resonator networks.
