Reduced rank extrapolation for multi-term Sylvester equations

TL;DR

This paper explores the use of reduced rank extrapolation (RRE) to accelerate stationary iterations solving multi-term Sylvester equations, demonstrating improved convergence and efficiency especially for large-scale problems.

Contribution

It provides theoretical convergence analysis and practical implementation strategies for RRE in multi-term Sylvester equations, including large-scale inexact methods.

Findings

RRE significantly accelerates convergence in multi-term Sylvester equations.

The approach reduces storage and computational costs.

Numerical experiments confirm the effectiveness of RRE in large-scale problems.

Abstract

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.