Factorized Krylov subspace methods for solving large Sylvester equations
For researchers in scientific computing, this provides a more efficient approach to solving large Sylvester equations, though it is an incremental improvement over existing methods.
This paper proposes a new framework for solving large Sylvester equations in low-rank format by reconstructing matrix-oriented Krylov subspace methods, achieving efficient computation and reduced memory requirements. Numerical experiments demonstrate effectiveness.
Krylov subspace methods, such as the Conjugate Gradient (CG) and BiCGSTAB methods, are widely used in scientific computing for solving linear systems. In this study, we propose a new framework for solving large Sylvester equations in a low-rank format by reconstructing matrix-oriented Krylov subspace methods. The framework realizes efficient algorithms that are mathematically equivalent to the matrix-oriented Krylov subspace methods by exploiting the mathematical properties of the Sylvester operator and the low-rank structure of the right-hand side. Specifically, by leveraging these properties, approximate solutions can be expressed in a low-rank factorized form, enabling efficient computation and reduced memory requirements. The effectiveness of our algorithms is demonstrated through numerical experiments.