Analysis of RCLUPPr: stability, robustness and acceleration
Abstract
In this work, we present a comprehensive rounding error analysis for RCLUPPr, a recently developed randomized CholeskyQR-type algorithm introduced in \cite{RCLUPP}. This method performs LU factorization with partial pivoting (LUPP faztorization) directly on a full-rank tall-skinny matrix X ∈ ℝm × n. Unlike RCLUPP in \cite{RCLUPP}, which applies matrix sketching prior to LUPP factorization, RCLUPPr deploys LUPP as an initial preconditioning step to significantly mitigate the propagation of error significantly. Our rigorous analysis demonstrates that RCLUPPr exhibits superior robustness when applied to the ill-conditioned matrices compared to other CholeskyQR-type algorithms in the high precision. Furthermore, we develop some practical strategies in the implementation to accelerate RCLUPPr. Extensive numerical experiments on the real-world problems validate our theoretical findings, showcasing the robustness and the efficiency of RCLUPPr across the single, double and the mixed-precision frameworks.
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BibTeX
@misc{guan2026analysis,
title = {{Analysis of RCLUPPr: stability, robustness and acceleration}},
author = {Haoran Guan and Zhenyu Zou and Yufeng Wei and Yipei Chen and Peiting You and Yuwei Fan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.15561},
eprint = {2607.15561},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.15561},
}
RIS
TY - UNPB
TI - Analysis of RCLUPPr: stability, robustness and acceleration
AU - Haoran Guan
AU - Zhenyu Zou
AU - Yufeng Wei
AU - Yipei Chen
AU - Peiting You
AU - Yuwei Fan
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2607.15561
UR - https://arxiv.org/abs/2607.15561
AB - In this work, we present a comprehensive rounding error analysis for RCLUPPr, a recently developed randomized CholeskyQR-type algorithm introduced in \cite{RCLUPP}. This method performs LU factorization with partial pivoting (LUPP faztorization) directly on a full-rank tall-skinny matrix X ∈ ℝ^m × n. Unlike RCLUPP in \cite{RCLUPP}, which applies matrix sketching prior to LUPP factorization, RCLUPPr deploys LUPP as an initial preconditioning step to significantly mitigate the propagation of error significantly. Our rigorous analysis demonstrates that RCLUPPr exhibits superior robustness when applied to the ill-conditioned matrices compared to other CholeskyQR-type algorithms in the high precision. Furthermore, we develop some practical strategies in the implementation to accelerate RCLUPPr. Extensive numerical experiments on the real-world problems validate our theoretical findings, showcasing the robustness and the efficiency of RCLUPPr across the single, double and the mixed-precision frameworks.
ER -