Centrala begrepp
The author introduces a novel framework for solving large-scale Lyapunov matrix equations using low-rank-modified Galerkin methods to achieve similar convergence rates to minimal-residual schemes with lower computational costs.
Sammanfattning
The content discusses the comparison between Galerkin, Pseudo-Minimal Residual (PMR), and Minimal Residual (MR) methods for solving large-scale Lyapunov matrix equations. The author proposes a new approach that modifies the Galerkin method to achieve better convergence rates similar to MR schemes while maintaining lower computational costs. Various numerical examples are presented to demonstrate the effectiveness of this new approach.
Key points include:
- Comparison of projection methods for solving large-scale Lyapunov equations.
- Introduction of a novel framework using low-rank modifications to improve convergence rates.
- Discussion on the computational cost and efficiency of different methods.
- Numerical examples showcasing the behavior and potential of the proposed approach.
Statistik
Galerkin: 1.2120e-02
PMR: 5.3767e-03
MR: 5.1983e-03