MI2D: Accelerating Matrix Inversion with 2-Dimensional Tile Manipulations

Abstract

Matrix inversion is critical in mathematics and scientific applications. Large-scale dense matrix inversion is especially challenging for modern computers due to its heavy dependency of matrix elements and the poor temporal data locality. In this paper, we propose a novel accelerator termed MI2D, which converts matrix inversion into regular matrix multiplications using 2-dimensional cross-tile operations and novel algorithms for efficient data reuse and computations. Our evaluations show that MI2D can be easily integrated with existing matrix engines in modern high-end CPU and NPU, and effectively improves matrix inversion with 2.7× speedup against Intel Skylake CPU, and 24× against NVIDIA RTX 2080 Ti.