A block Recycled GMRES method with investigations into aspects of solver performance
This work addresses the need for efficient iterative solvers for large-scale linear systems, but the contribution is incremental as it extends an existing method.
The authors propose a block Krylov subspace version of the GCRO-DR method for solving linear systems, demonstrating improved convergence and data movement efficiency in numerical experiments.
We propose a block Krylov subspace version of the GCRO-DR method proposed in [Parks et al.; SISC 2005], which is an iterative method allowing for the efficient minimization of the the residual over an augmented Krylov subspace. We offer a clean derivation of our proposed method and discuss methods of selecting recycling subspaces at restart as well as implementation decisions in the context of high-performance computing. Numerical experiments are split into those demonstrating convergence properties and those demonstrating the data movement and cache efficiencies of the dominant operations of the method, measured using processor monitoring code from Intel.