Dual-Triangular QR Decomposition with Global Acceleration and Partially Q-Rotation Skipping

Abstract

Efficient matrix operations have been deemed keys to efficient data analysis. Dual-Triangular QR Decomposition (DT-QRD) is a critical component in Tall and skinny QR decomposition (TS-QRD), which is a widely-used matrix operation with various applications, such as data compression and feature extraction. In order to accelerate DT-QRD, in this paper, we propose a new acceleration framework, including Global Acceleration Schemes, and Partially $\boldsymbol{Q}$ -rotation Skipping, which utilize the special DT structure in both $\mathbf{Q}$ and $\mathbf{R}$ matrix to reduce the latency and computation resource. Further, we employ the Systolic-Array Based Architecture (1D & 2D) for implementation to reduce the memory usage. Experimental results manifest that our framework achieves $169.70\times\ (\mathbf{1}\mathbf{D})$ and $250.13\times\ (\mathbf{2}\mathbf{D})$ speedup.