Parallel Computing Matrix Operations

With development of science and technology, High Performance Computing has been seen in many fields. As a scientific calculation method, numerical calculation could solve many practical engineering problems quickly by integrating with parallel computing. The numerical calculation is also called numerical analysis or numerical numerical method. Since the number has been created,we need the calculation. Numerical calculation provides relative algorithms and theory for all kinds of problem about arithmetic. By computational tools, some complicated math problems could be solved numerically.One of the numerical study content is matrix which includs matrix calculations and solution via matrix eigenvalues.Solution via matrix not only can solve some linear programming or nolinear programming and complex equations problem, etc, but also play an important role in subjects such ad aerospace civil engineering meteorological and physics,etc.It can be said that scientific research has been can't without matrix calculation.For better design research to high-performance computer parallelalgorithm, related departments defined a standard of massagepassing—MPI(massage passing Interface), in the above this standarddevelopment of massage passing software MPICH, making the MPI sdandard can be widely realized. Because of the MPICH excellent performance and operability,it get the nod of most programmers and also is the most popular applied the most wide hair negotiable parallel environment and very harmonious solved the communication problems in between of large-scale computer group.This article further subdivides matrixes and integrate the parallelalgorithm with the matrix algorithm.Under the MPI sdandard build computer group parallel environment and by parallel QR decomposition and algorithm,this paper has realized decomposition of the matrix and solved the linear equation all solution.This paper,first of all introducted briefly the development of parallel computer, steted the development history of high-performancecomputer,narrated the now most popular and most widely massage passings tandard MIP and under the MIP build parallel programming environment, build a computer group systerm through the windows xp systerm combined with MPICH build a parallel programming environment.In the next introduced the traditional serial matrix calculation algorithm and parallelization calcution for matrix computation, use parallel algorithm combined with matrix decomposition decomposed the matrix and solve thecharacteristic value, in the last analysis and realized the entire program.Finally,through the parallel algorithm combined with matrix QRdecompsition and Jordan transformation solving to optimizing the general N row N column matrix, thrioughthe experimental results to the traditionalserial algorithm and parallel algorithm contrast analysis,reflecton theparallel algorithm for the the operation efficiency of all program haveimproved signficantly.