Fast Hybrid Solution of Algebraic Systems

We propose and analyze the error and timing of solvers consisting of both analog and digital circuitry for sparse linear systems of equations. We obtain high speed, but low precision from the analog circuits. We combine this 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. We also apply the hybrid circuit to a standard multilevel algorithm.