Performing analog computations with metastructures is an emerging wave-based paradigm for solving mathematical problems.For such devices,one major challenge is their reconfigurability,especially without the need for a priori mathematical computations or computationally-intensive optimization.Their equation-solving capabilities are applied only to matrices with special spectral(eigenvalue)distribution.Here we report the theory and design of wave-based metastructures using tunable elements capable of solving integral/differential equations in a fully-reconfigurable fashion.We consider two architectures:the Miller architecture,which requires the singular-value decomposition,and an alternative intuitive direct-complex-matrix(DCM)architecture introduced here,which does not require a priori mathematical decomposition.As examples,we demonstrate,using system-level simulation tools,the solutions of integral and differential equations.We then expand the matrix inverting capabilities of both architectures toward evaluating the generalized Moore-Penrose matrix inversion.Therefore,we provide evidence that metadevices can implement generalized matrix inversions and act as the basis for the gradient descent method for solutions to a wide variety of problems.Finally,a general upper bound of the solution convergence time reveals the rich potential that such metadevices can offer for stationary iterative schemes.
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