Fast Hybrid Solution of Algebraic Systems

Abstract

The error and timing of solvers consisting of both analog and digital circuitry for sparse linear systems of equations are proposed and analyzed. High speed but low precision is obtained from the analog circuits. This is combined with low speed but high precision from the digital circuits. The hybrid circuit should be faster than digital circuits alone. As a preconditioner to standard iterative solution methods, the hybrid circuit makes the cost of the preconditioning step negligible. The hybrid circuit is also applied to a standard multilevel algorithm.