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arXiv · 2508.00722

Towards a mixed-precision ADI method for Lyapunov equations

Jonas Schulze·Jens Saak
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Abstract

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 H2 norm of a descriptor system, low- or mixed-precision variants of the ADI can be quite competitive

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Jonas Schulze, Jens Saak. 2025-08-01. Towards a mixed-precision ADI method for Lyapunov equations. https://arxiv.org/abs/2508.00722

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