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Hierarchical Matrix Operations on GPUs: Matrix-Vector Multiplication and Compression by Boukaram, Wajih Halim; Turkiyyah, George; Keyes, David E. is a scholarly article available to read on EtoBox.

What is Hierarchical Matrix Operations on GPUs: Matrix-Vector Multiplication and Compression about?

Hierarchical matrices are space and time efficient representations of dense matrices that exploit the low rank structure of matrix blocks at different levels of granularity. The hierarchically low rank block partitioning produces representations that can be stored and operated on in near-linear complexity instead of the usual polynomial complexity of dense matrices. In this paper, we present high performance implementations of matrix vector multiplication and compression operations for the $\mathcal{H}^2$ variant of hierarchical matrices on GPUs. This variant exploits, in addition to the hierarchical block partitioning, hierarchical bases for the block representations and results in a scheme that requires only $O(n)$ storage and $O(n)$ complexity for the mat-vec and compression kernels. These two operations are at the core of algebraic operations for hierarchical matrices, the mat-vec being a ubiquitous operation in numerical algorithms while compression/recompression represents a key building block for other algebraic operations, which require periodic recompression during execution. The difficulties in developing efficient GPU algorithms come primarily from the irregular tree dat

Author

Boukaram, Wajih Halim; Turkiyyah, George; Keyes, David E.

Published

2019

Language

EN