Parallel Tall-and-Skinny QR Factorization Based on LU-CholeskyQR Algorithm - Uchino, Yuki; Imamura, Toshiyuki (Proceedings / IEEE International Conference on Cluster Computing, 2025)
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.