The advent of memristive devices offers a promising avenue for efficient and scalable analog computing, particularly for linear algebra operations essential in various scientific and engineering applications. This paper investigates the potential of memristive crossbars in implementing matrix inversion algorithms. We explore both static and dynamic approaches, emphasizing the advantages of analog and in-memory computing for matrix operations beyond multiplication. Our results demonstrate that memristive arrays can significantly reduce computational complexity and power consumption compared to traditional digital methods for certain matrix tasks. Furthermore, we address the challenges of device variability, precision, and scalability, providing insights into the practical implementation of these algorithms.

翻译：忆阻器件的出现为高效且可扩展的模拟计算提供了一条前景广阔的途径，尤其适用于各类科学与工程应用中至关重要的线性代数运算。本文研究了忆阻交叉阵列在实现矩阵求逆算法方面的潜力。我们探讨了静态与动态两种方法，重点分析了模拟计算与内存内计算在乘法以外的矩阵运算中的优势。研究结果表明，对于特定矩阵任务，忆阻阵列相较于传统数字方法能显著降低计算复杂度与功耗。此外，我们针对器件变异性、精度与可扩展性等挑战进行了探讨，为这些算法的实际应用提供了见解。