A class of low-rank short recurrences for nonsymmetric linear matrix equations

Abstract

We propose a new class of short matrix recurrences for the solution of nonsymmetric linear equations of the type $\mathbf{A}_1\mathbf{X}\mathbf{B}_1+\ldots+\mathbf{A}_p\mathbf{X}\mathbf{B}_p=CD^T$. Building on ideas underpinning the recently introduced subspace conjugate gradient algorithm, we derive low-rank short recurrences that generalize one-dimensional subspace projection methods to the nonsymmetric matrix equation setting. To limit memory consumption and maximize computational efficiency, rank truncation strategies and modern randomization procedures are incorporated into the proposed algorithms. 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.