ABOUT THE REAL POSSIBILITIES OF MODERN COMPUTING SYSTEMS FOR DISTRIBUTED MULTIPLICATION OF LARGE-DIMENSIONAL MATRICES

Abstract

The needs of practice constantly require improving the performance of computing systems. For quite a long time, multiprocessor systems have been the main way to build ultra-high performance computing systems. When creating such systems, many difficult problems arise. They are related to the need to parallelize the computing process in order to efficiently load the system processors, overcome conflicts when several processors try to use the same system resource, reduce the impact of conflicts on system performance, etc. With microelectronics overcoming the milestone of a billion transistors on a silicon chip, a new paradigm of multicore processors has emerged. At the same time, the problem of the ratio of multicore and multithreading in modern computers arose. This is due to the dilemma of preference between them. A multicore processor contains two or more electronic computing cores placed on a single semiconductor crystal. Each core of a multicore processor is a full-fledged microprocessor. Multicore is an obvious and traditional method of distributed solution of many complex tasks. But this cannot be said about multithreading, which relies on the use of very fast cache memory associated with the main memory and serves to reduce the average access time to the main memory of the processor. The relative novelty of modern approaches to the construction of computing systems requires comparative experimental studies of their capabilities. A promising and convenient mathematical object for these purposes is the distributed multiplication of matrices of large dimensions. The article presents practical results of distributed multiplication of square matrices with sizes from 300*300 to 2000*2000 and randomly generated values of elements in the matrices in the range from -100 to +100. Based on the experimental data presented in the corresponding tables and graphs, hyperbolic relations are obtained for the dependence of the matrix multiplication time on the number of virtual machines (cores) in the laptop used. Similar results were obtained by multiplying square matrices on single-processor computers connected to a local network. Analytical expressions in this case also represent hyperbolic time dependencies. But the numerical values in them significantly exceed those for the hyperbolic formula obtained for the laptop. Based on the results obtained, the conducted research allows us to conclude that the use of a single-processor computer connected to a local network for multiplying matrices of large dimensions is inferior to the performance of a laptop. This is due to the significant time spent moving data over the local network.