Study On FPGA-based Parallel Computing Of The Matrix Eigenvalues

With the development of digital technology，more requirements of the capability ofprocessing the data have also been put forward, and the common array signal inengineering application also needs a faster processing speed. Matrix eigenvaluecharacterizes many features of the matrix and plays an important role in matrix analysis.At the same time, the improvement of traditional single-processor system performanceis limited. From another perspective, the multi-processor parallel computation improvesthe processing speed of the system.Therefore, based on Xilinx FPGA, this paper designs an embedded dual coresystem in order to get the parallel solving of matrix eigenvalue, and compared withserial computation on single-core system.In this paper, the main work and achievements are as follows.①Parallel computation: Study the basic concept of parallel computing, the basicmethod of performance evaluation in parallel and the basic conditions of implementingthe parallel algorithm. It introduces typical parallel computer model, such as thesymmetric multiprocessor system, distributed storage systems, distributed sharedmemory system, cluster system, etc. And it analyzes PRAM, BSP, LogP, hierarchicalstorage and other commonly used parallel computing model. Based on parallelcomputing model, it introduces the general design process of parallel algorithm incombination with commonly used parallel algorithm design techniques.②Embedded multi-core systems：Understand the main factors of embeddedreal-time system design and key indicators of evaluating real-time performance. Itintroduces the Microblaze soft core and PowerPC hard core. It gives the detaileddescription on the performance and use of the characteristics of the OPB, PLB, XCL,FSL, LMB bus ISE10.1Development Kit support mechanisms. It mades a detailedintroduction to the Mailbox, Mutex, Shared Memory, Interrupt, PLB Bridge and othercommon communication mechanisms based on Xilinx FPGA embedded multi-coresystem design..③Matrix eigenvalue calculation: The mathematical and physical meanings of theMatrix eigenvalue are briefly discussed and some basic properties of the matrixeigenvalue are listed. It analyzes the mathematical model of Jacobi algorithm andone-side rotation algorithm of symmetric matrix eigenvalue calculation, and serial and parallel implementation method. It analyzes the mathematical model of the QRalgorithm of the general matrix eigenvalue calculation and serial and parallelimplementation method. Verify and compare the various algorithms by using visual c++and MPI library.④Based on the dual-core system algorithm implementation: introduces the maintechnical features of the Xilinx Spartan-3E development board and using ISE10.1Development Kit designed single-core systems and dual-core systems based on theMailbox, Mutex communication mechanism. Design FPGA-based matrix eigenvaluecalculation algorithm, serial computing in the single core system, parallel computing inthe dual-core system. Using a plurality of matrices to verify the feasibility of thealgorithm, summarize the advantages of parallel computing by comparing.