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A Novel Randomized XR-Based Preconditioned CholeskyQR Algorithm

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arxiv 2111.11148 v2 pith:4UQ4FSR3 submitted 2021-11-22 math.NA cs.NA

Yuwei Fan , Yixiao Guo , Ting Lin This is my paper · ORCID
classification math.NAcs.NA
keywords randomizedcholeskyqralgorithmconditiondecompositionframeworkmethodsnumber
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CholeskyQR is a simple and fast QR decomposition via Cholesky decomposition, while it has been considered highly sensitive to the condition number. In this paper, we provide a randomized preconditioner framework for CholeskyQR algorithm. Under this framework, two methods (randomized LU-CholeskyQR and randomized QR-CholeskyQR) are proposed and discussed. We prove the proposed preconditioners can effectively reduce the condition number, which is also demonstrated by numerical tests. Abundant numerical tests indicate our methods are more stable and faster than all the existing algorithms and have good scalability.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. GPU-Parallelizable Randomized Sketch-and-Precondition for Linear Regression using Sparse Sign Sketches

    cs.DS 2025-06 accept novelty 6.0 of 10

    A GPU implementation of sparse-sign-sketch-and-precondition for linear regression scales well on up to 8 NVIDIA A100s, with a novel rejection-sampling sketch generator.

  2. RCLUPPr: a new randomized CholeskyQR with LU preconditioning

    math.NA 2026-07 conditional novelty 5.0 of 10

    RCLUPPr, a randomized CholeskyQR variant with LU preconditioning, is shown stable and more applicable to ill-conditioned tall-skinny matrices than prior CholeskyQR-type algorithms.

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