Fast Solution of Linear Systems with Analog Resistive Switching Memory (RRAM)

The in-memory solution of linear systems with analog resistive switching memory in one computational step has been recently reported. In this work, we investigate the time complexity of solving linear systems with the circuit, based on the feedback theory of amplifiers. The result shows that the computing time is explicitly independent on the problem size N, rather it is dominated by the minimal eigenvalue of an associated matrix. By addressing the Toeplitz matrix and the Wishart matrix, we show that the computing time increases with log(N) or N1/2, respectively, thus indicating a significant speed-up of in-memory computing over classical digital computing for solving linear systems. For sparse positive-definite matrix that is targeted by a quantum computing algorithm, the in-memory computing circuit also shows a computing time superiority. These results support in-memory computing as a strong candidate for fast and energy-efficient accelerators of big data analytics and machine learning.