Reduced rank extrapolation for multi-term Sylvester equations
This work addresses computational efficiency for large-scale linear algebra problems, but it is incremental as it applies an existing acceleration technique to a specific equation type.
The paper tackles accelerating stationary iterations for multi-term Sylvester equations using reduced rank extrapolation (RRE), resulting in substantial gains in convergence speed that reduce storage and computing time, as shown in numerical experiments.
We investigate the acceleration of stationary iterations for multi-term Sylvester equation by means of reduced rank extrapolation (RRE). Theoretical convergence results and implementations are provided for both small and large-scale problems. For the large-scale problems, an inexact non-stationary iteration is discussed, which makes use of low-rank matrix approximations. Numerical experiments illustrate the potential of the RRE acceleration which often leads to a substantial gain in convergence speed and therefore reducing the consumption of storage and computing time.