Toward a Mixed‐Precision ADI Method for Lyapunov Equations

We apply mixed‐precision to the low‐rank Lyapunov ADI (LR‐ADI) by performing certain aspects of the algorithm in a lower working precision. Namely, we accumulate the overall solution, solve the linear systems comprising the ADI iteration, and store the inner low‐rank factors of the residuals in various combinations of IEEE 754 single and double precision. We empirically test our implementation on Lyapunov equations arising from first‐ and second‐order descriptor systems. For the first‐order examples, accumulating the solution in single‐precision yields an almost‐as‐small residual as for the double‐precision solution. For certain applications, like computing the norm of a descriptor system, low‐ or mixed‐precision variants of the ADI can be quite competitive.