A performance analysis of computing the LU and the QR matrix decompositions on the CPU and the GPU

Abstract

We present an analysis of time efficiency of five different implementations of the LU and the QR decomposition of matrices performed on central processing unit (CPUs) and graphics processing units (GPUs). Three of the considered implementations, developed using the Eigen C++ library, Intel MKL, and MATLAB are executed on a multi-core CPU. The remaining two implementations are processed on a GPU and employ MATLAB's Parallel Computing Toolbox and Nvidia CUDA augmented with the cuSolver library. Computation times are compared using randomly generated single- and double-precision floating-point matrices. The experiments for the LU decomposition show that the two GPU implementations offer best performance for matrices that can fit into the GPU global memory. For larger LU decomposition problem instances, Intel MKL on the CPU is found to be the fastest approach. Furthermore, Intel MKL also proves to be the fastest method for computing QR decomposition for all considered sizes of matrices.