Parallel Tall-and-Skinny QR Factorization Based on LU-CholeskyQR Algorithm

We present optimal parallel QR factorization algorithms with reduced communication overhead. QR factorization is widely applied to solve various problems in numerical linear algebra. Our focus is on problems involving dense tall-and-skinny matrices in large-scale parallel distributed memory systems....

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Bibliographic Details
Published in:Proceedings / IEEE International Conference on Cluster Computing pp. 1 - 10
Main Authors: Uchino, Yuki, Imamura, Toshiyuki
Format: Conference Proceeding
Language:English
Published: IEEE 02.09.2025
Subjects:
Benchmark testing
Cluster computing
Clustering algorithms
communication-avoiding algorithm
Costs
Data communication
Error analysis
High performance computing
Linear algebra
LU factorization
Numerical stability
Parallel algorithms
tall-and-skinny QR factorization
ISSN:2168-9253
Online Access:Get full text
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Summary:We present optimal parallel QR factorization algorithms with reduced communication overhead. QR factorization is widely applied to solve various problems in numerical linear algebra. Our focus is on problems involving dense tall-and-skinny matrices in large-scale parallel distributed memory systems. Reducing data communication is essential for achieving high performance in parallel algorithms because the communication cost is much greater than the computation cost. To date, several QR factorization algorithms have been optimized to reduce communication costs. This paper provides alternative parallel QR factorization algorithms based on the LU-CholeskyQR algorithm. Numerical experiment results demonstrated the accuracy and performance of the developed algorithms against benchmarks. The results indicate that the new algorithms are numerically stable even for ill-conditioned problems, and some of these algorithms are faster than other conventional algorithms.
ISSN:2168-9253
DOI:10.1109/CLUSTER59342.2025.11186492