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PreprintCC BY 4.0arXiv

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

  • Davide Palitta
  • Catherine E. Powell
  • Valeria Simoncini
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Abstract

We propose a new class of short matrix recurrences for the solution of nonsymmetric linear equations of the type A1XB1+…+ApXBp=CDT. 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.

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Cite

BibTeXRIS
BibTeX
@misc{palitta2026class,
  title = {{A class of low-rank short recurrences for nonsymmetric linear matrix equations}},
  author = {Davide Palitta and Catherine E. Powell and Valeria Simoncini},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.01276},
  eprint = {2605.01276},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.01276},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A class of low-rank short recurrences for nonsymmetric linear matrix equations
AU  - Davide Palitta
AU  - Catherine E. Powell
AU  - Valeria Simoncini
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2605.01276
UR  - https://arxiv.org/abs/2605.01276
AB  - We propose a new class of short matrix recurrences for the solution of nonsymmetric linear equations of the type A_1XB_1+…+A_pXB_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.
ER  -