Accelerating the solution of linear systems of equations is critical due to their central role in numerous applications, such as numerical simulations, data analytics, and machine learning. This paper presents an analog solver circuit designed to accelerate the solution of symmetric positive definite (SPD) linear systems of equations. The proposed design leverages noninverting operational amplifier configurations to create a negative resistance circuit, effectively modeling any symmetric system. The paper details the principles behind the design, optimizations of the system architecture, and numerical results that demonstrate the robustness of the design. The findings reveal that the proposed system solves symmetric diagonally dominant (SDD) matrices with O(1) complexity, achieving the theoretical maximum speed as the circuit relies solely on resistors. For non-diagonally dominant SPD systems, the solution speed depends on matrix properties, specifically eigenvalues and diagonal dominance deviation, but remains independent of the size of the matrix.

翻译：线性方程组的求解加速至关重要，因为其在数值模拟、数据分析和机器学习等众多应用中处于核心地位。本文提出一种模拟求解电路，旨在加速对称正定线性方程组的求解。该设计利用同相运算放大器配置构建负电阻电路，从而有效模拟任意对称系统。论文详细阐述了设计原理、系统架构优化以及验证设计鲁棒性的数值结果。研究结果表明，所提出的系统能以O(1)复杂度求解对称对角占优矩阵，由于电路仅依赖电阻元件，达到了理论最大求解速度。对于非对角占优的对称正定系统，求解速度取决于矩阵特性（特别是特征值和对角占优偏差），但仍保持与矩阵规模无关的特性。