Efficient parallel algorithms for multi-dimensional matrix operations

Abstract

Matrix operations are the core of many linear systems. Efficient matrix multiplication is critical to many numerical applications, such as climate modeling, molecular dynamics, computational fluid dynamics and etc. Much research work has been done to improve the performance of matrix operations. However, the majority of these works is focused on two-dimensional (2D) matrix. Very little research work has been done on three or higher dimensional matrix. Recently, a new structure called Extended Karnaugh Map Representation (EKMR) for n-dimensional (nD) matrix representation has been proposed, which provides better matrix operations performance compared to the Traditional matrix representation (TMR). The main idea of EKMR is to represent any nD matrix by 2D matrices. Hence, efficient algorithms design for nD matrices becomes less complicated. Parallel matrix operation algorithms based on EKMR and TMR are presented. Analysis and experiments are conducted to assess their performance. Both our analysis and experimental result show that parallel algorithms based on EKMR outperform those based on TMR.