Floating Point Compression of Hierarchical Matrix Formats and its Impact on Matrix-Vector Multiplication

TL;DR

This paper investigates how floating point compression of hierarchical matrix formats can reduce memory usage and improve the performance of matrix-vector multiplication, a key operation in many iterative algorithms.

Contribution

It introduces methods for compressing hierarchical matrices using floating point techniques and analyzes their impact on matrix-vector multiplication performance.

Findings

Floating point compression reduces memory footprint of hierarchical matrices.

Compressed formats lead to faster matrix-vector multiplication.

Performance gains are significant on parallel systems.

Abstract

Matrix-vector multiplication forms the basis of many iterative solution algorithms and as such is an important algorithm also for hierarchical matrices which are used to represent dense data in an optimized form by applying low-rank compression. However, due to its low computational intensity, the performance of matrix-vector multiplication is typically limited by the available memory bandwidth on parallel systems. With floating point compression the memory footprint can be optimized, which reduces the stress on the memory sub system and thereby increases performance. We will look into the compression of different formats of hierachical matrices and how this can be used to speed up the corresponding matrix-vector multiplication.