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arXiv · 2605.28274

Factorized Krylov subspace methods for solving large Sylvester equations

Yuki Satake·Takeshi Fukaya·Tomohiro Sogabe·Shao-Liang Zhang
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Abstract

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.

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Yuki Satake, Takeshi Fukaya, Tomohiro Sogabe, Shao-Liang Zhang. 2026-09-14. Factorized Krylov subspace methods for solving large Sylvester equations. https://arxiv.org/abs/2605.28274

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