INdAM Workshop: Low-rank Structures and Numerical Methods in Matrix and Tensor Computations

Extrapolation in nonstationary iterations for matrix equations

Sep 5, 2025, 11:00 AM

30m

Palazzone di Cortona

Talk Morning Session

Speaker

Patrick Kürschner (Leipzig University of Applied Sciences (HTWK Leipzig))

Description

Reduced rank extrapolation (RRE) [1,2] can be used to accelerate convergent vector sequences. These sequences are often generated by an iterative process to solve algebraic equations.
In this presentation, I discuss the generalization of this extrapolation framework to sequences of low-rank matrices which are generated by iterative methods for large-scale matrix equations, such as, e.g., low-rank alternating directions implicit methods for Lyapunov and Riccati equations [3]. Special emphasis will also be given to inserting these RRE approaches into nonstationary iterations [4] for general linear matrix equation.

References

1. R. P. Eddy: Extrapolating to the limit of a vector sequence. In Information linkage between applied mathematics and industry, Academic Press, Cambridge, MA, 1979.
2. A. Sidi: Efficient implementation of minimal polynomial and reduced
   rank extrapolation methods. J. Comput. Appl. Math., 1991.
3. P. d. Boef, P. Kürschner, X. Liu, J. Maubach, J. Saak, W. Schilders, J. Schulze, N. v. d. Wouw: Generalizing Reduced Rank Extrapolation to Low-Rank Matrix Sequences, Arxiv preprint 2502.09165, 2025.
4. S. D. Shank, V. Simoncini and D. B. Szyld: Efficient low-rank solutions of Generalized Lyapunov equations, Numerische Mathematik, 2016