Research And Implementation On Matrix Parallel Algorithm Based On MPI

By now, together with scientific experiments and scientific theory, scientificcomputing constitutes the three major scientific methods of scientific research. At thesame time, there emerge a series of huge, time-limited numerical problems in the fieldof engineering and scientific research, such as the data analysis of satellite images,global climate forecasting, nuclear fusion, large-scale econometric models, and thehuman genes. These topics in science and technology with the explosive growth ofcomputing make a strong challenge for the traditional serial computingtechnology—Von Neumann, while boosting huge demand for high-performancecomputing.In image processing, digital signal filtering, weather forecasting, networkrouting, intelligent traffic system, linear programming, Fourier transform, thematrixes are always used to describe and store the large-scale logical structural data.And the related applications are too numerous to mention, so matrix operation is oneof the most basic and important skills in scientific and engineering computing. IN lasttwenty years, the researching of parallel algorithms in this area has been very active.In this paper, by the means of relevant theoretical knowledge’s about virtualmachine, network and operating system, I built a four-virtual machine cluster system,with each operating system is Linux and MPICH2as the parallel environment.Parallel programs in the papers are executed based on this platform.This paper describes a parallel cluster hardware and software environment,including the parallel computer architecture, cluster machine model system and MPIprogramming interface model.By the means of abstract computing models, I have done a lot of research aboutparallel algorithms of the large dimension of matrix multiplication algorithm, which isvery important and difficult. Algorithms about matrix multiplication are divided intostrip-dividing and chess-dividing, strip-dividing algorithms can be divided in rows or columns, depending on which we can find out the different algorithms. And thechess-dividing algorithms include Fox, Cannon algorithms and so on.In the exploration in the implementation of the algorithms, I focus on theperformance by optimizing these parallel programs, and analyze and compare therunning results.In the end, a small-scale complete virtual clusters system is built, and the paralleltechnology is used to solve specific problems on the platform.Matrix multiplication algorithms are applied to shortest path problem andconvolution problem and the satisfactory results are achieved by calling the MPIlibrary.