Analog Matrix Inversion Circuit Design for Solving Tridiagonal Linear Systems: A Compact and Decoupled Approach

Recently, analog matrix inversion circuits (INV) have demonstrated significant advantages in solving matrix equations. However, solving large-scale sparse tridiagonal linear systems (TLS) using full-scale INV introduces considerable zero regions redundancy and interconnection factors. To address this issue, this article proposes a dedicated INV for solving TLS. The TLS is reformulated into a tightly coupled matrix equation system (CMES), effectively eliminating the zero regions within the array of INV. Very large-scale TLS (VLTLS) are processed by the proposed decoupled INV equipped with a spike algorithm engine. Compared with the general INV, the proposed circuit offers enhanced advantages in compactness and scalability. PSpice-based simulation experiments demonstrate that the proposed circuit achieves a solving accuracy of over 99%. Comprehensive nonidealities are also evaluated, with a curve-fitting accuracy of 98.41%. Utilizing commercial operational amplifier (OA) models, the proposed circuit achieves microsecond-level computation speed, offering a two-order-of-magnitude acceleration compared to conventional software-based approaches. Furthermore, the solution of a 1-D diffusion equation with 1024 internal nodes verifies the effectiveness of the proposed circuit in solving large-scale TLS.