Analog Solutions of Systems of Linear Equations on a Configurable Platform

摘要

Even though analog computation is better suited for differential equation solutions (ODE, PDE), sometimes it needs to solve systems of linear equations. This discussion focuses on analog solutions of linear equation systems, implemented on a configurable platform. Digital systems rely on solving linear equations as the fundamental numerical computation. Systems of linear equations are used to solve static circuits illustrating that at least a reduced class of analog physical linear system computation should be possible. The analog approaches utilize iterative techniques, setting up a set of ODEs to solve the system of linear equations, rather than relying on matrix decompositions (e.g. LU decomposition). The approach allows for multiple potential configurable circuit approaches. A set of amplifier networks has been designed to demonstrate the solutions for different matrices. These techniques provide energy-efficient continuous-time solutions. The resulting algorithm has been studied considering the analog numerical analysis for the solution and convergence time.