Analysis of randomized CholeskyQR for sparse matrices

Fuente: arXiv
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Main Authors: Guan, Haoran, Fan, Yuwei
Format: Preprint
Published: 2025
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author Guan, Haoran
Fan, Yuwei
author_facet Guan, Haoran
Fan, Yuwei
contents This work is about rounding error analysis of randomized CholeskyQR-type algorithms for sparse matrices. We often encounter QR factorization of the sparse matrices in many real problems. In this work, we focus on some typical CholeskyQR-type algorithms with matrix sketching, which is a popular randomized technique in recent years. We build a new model of the sparse matrices and provide rounding error analysis of randomized CholeskyQR-type algorithms for the sparse cases with this model. We make comparison between the bounds with different models of sparsity both theoretically and experimentally. Numerical experiments show some new phenomena of randomized CholeskyQR-type algorithms for the sparse cases, which do not occur in the common sparse cases. We also test the applicability, accuracy, efficiency and robustness of randomized CholeskyQR-type algorithms for sparse matrices.
format Preprint
id arxiv_https___arxiv_org_abs_2506_04208
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Analysis of randomized CholeskyQR for sparse matrices
Guan, Haoran
Fan, Yuwei
Numerical Analysis
65F25, 15A23, 65F30, 65G50
This work is about rounding error analysis of randomized CholeskyQR-type algorithms for sparse matrices. We often encounter QR factorization of the sparse matrices in many real problems. In this work, we focus on some typical CholeskyQR-type algorithms with matrix sketching, which is a popular randomized technique in recent years. We build a new model of the sparse matrices and provide rounding error analysis of randomized CholeskyQR-type algorithms for the sparse cases with this model. We make comparison between the bounds with different models of sparsity both theoretically and experimentally. Numerical experiments show some new phenomena of randomized CholeskyQR-type algorithms for the sparse cases, which do not occur in the common sparse cases. We also test the applicability, accuracy, efficiency and robustness of randomized CholeskyQR-type algorithms for sparse matrices.
title Analysis of randomized CholeskyQR for sparse matrices
topic Numerical Analysis
65F25, 15A23, 65F30, 65G50
url https://arxiv.org/abs/2506.04208