Randomised sketching of parametric linear systems

With current limitations in technology scaling and increasing processor power consumption, approximate computing techniques are being explored to meet the stringent time and memory constraints. One such approach is to explore randomised ‘data sketching’ to subsample the algebraic operations and considerably reduce compute complexity. Focusing on the paradigm of large-scale parametric linear systems we develop a direct solver based on subspace projection and randomisation suitable to the multi-query setting. Our algorithm incorporates efficient, parameter oblivious sampling and a subsequent control variates-based correction to reduce the variance of the sketched system. We validate the performance of the scheme using numerical experiments, based on a system arising from application of the finite element method.