A class of low-rank short recurrences for nonsymmetric linear matrix equations
This work addresses the need for efficient iterative solvers for large-scale nonsymmetric linear matrix equations, which are common in scientific computing and engineering.
The paper proposes a new class of short matrix recurrences for solving nonsymmetric linear matrix equations, combining local subspace projection, rank truncation, and randomization to improve convergence and limit memory. Experiments on a benchmark and a challenging diffusion problem demonstrate the method's potential.
We propose a new class of short matrix recurrences for the solution of nonsymmetric linear equations of the type $\mathbf{A}_1\mathbf{X}\mathbf{B}_1+\ldots+\mathbf{A}_p\mathbf{X}\mathbf{B}_p=CD^T$. These iterative methods combine local subspace projection to speed up convergence with rank truncation strategies and randomization procedures to limit memory consumption. Computational experiments on a benchmark problem as well as a challenging discretized mixed formulation of a diffusion equation with random inputs illustrate the potential of the proposed methodology.