Fast and Memory Efficient Strassen’s Matrix Multiplication on GPU Cluster

Prior implementations of Strassen's matrix multiplication algorithm on GPUs traded additional workspace in the form of global memory or registers for time. Although Strassen's algorithm offers a reduction in computational complexity as compared to the classical algorithm, the memory overhead associated with the algorithm limits its practical utility. While there were past attempts at reducing the memory footprint of Strassen's algorithm by compromising parallelism, no prior implementation, to our knowledge, was able to hide the workspace requirement successfully. This thesis presents an implementation of Strassen's matrix multiplication in CUDA, titled Multi-Stage Memory Efficient Strassen (MSMES), that eliminates additional workspace requirements by reusing and recovering input matrices. MSMES organizes the steps involved in Strassen's algorithm into five stages where multiple steps in the same stage can be executed in parallel. Two additional stages are also discussed in the thesis that allows the recovery of the input matrices. Unlike previous works, MSMES has no additional memory requirements irrespective of the level of recursion of Strassen's algorithm. Experiments performed with MSMES (with the recovery stages) on NVIDIA Tesla V100 GPU and NVIDIA GTX 1660ti GPU yielded higher compute performance and lower memory requirements as compared to the NVIDIA library function for double precision matrix multiplication, cublasDgemm. In the multi-GPU adaptation of matrix multiplication, we explore the performance of a Strassen-based and a tile-based global decomposition scheme. We also checked the performance of using MSMES and cublasDgemm for performing local matrix multiplication with each of the global decomposition schemes. From the experiments, it was identified that the combination of using Strassen-Winograd decomposition with MSMES yielded the highest speedup among all the tested combinations

The deep space network

The facilities, programming system, and monitor and control system for the deep space network are described. Ongoing planetary and interplanetary flight projects are reviewed, along with tracking and ground-based navigation, communications, and network and facility engineering