Year: 2024
Type: article
Abstract: Hierarchical low-rank approximation of dense matrices can reduce the complexity of their factorization from [Formula: see text] to [Formula: see text]. However, the complex structure of such hierarchical matrices makes them difficult to parallelize. The block size and ranks can vary between the sub-blocks, which creates load imbalance. The dependency between the sub-blocks during factorization results in serialization. Since many sub-blocks are low-rank, their small computational load exposes the overhead of runtime systems. The combination of these factors makes it challenging to implement these methods on GPUs. In this work, we show that dense matrices can be factorized with linear complexity, while extracting the potential parallelism of GPUs. This is made possible through the [Formula: see text]-ULV factorization, which removes the dependency on trailing sub-matrices.
Authors: Qianxiang Ma, Rio Yokota
Institution: Tokyo Institute of Technology
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: 低ランク構造行列法の適用範囲拡大と多様な計算アーキテクチャの活用, Next-generation high-performance linear solver for future computational science and engineering, Construction of numerical linear algebra based on lattice H-matrices and its high-performance implementation on modern architectures, G6718509927, Application of Unconventional Linear Algebra Techniques to Continuous Learning in Supergiant Neural Networks, Fast and accurate eigenvalue calculations by hierarchical low-rank approximation and its application to large-scale electronic structure calculations
OpenAlex ID: W4393855615