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The Study of Parallel Algorithms for the Solution of Special Structured Large Linear System of Equations under Distributed Memory Environment

Author: LuoZhiGang
Tutor: LiXiaoMei
School: People's Liberation Army National Defense University of Science and Technology
Course: Computer Science and Technology
Keywords: Distributed Storage Tridiagonal equations Cycle Block method Toeplitz Triangular equations Sparse linear equations Krylov subspace methods s step-by-step approach Parallel computing
CLC: TP301.6
Type: PhD thesis
Year: 2000
Downloads: 545
Quote: 9
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Abstract

The typical structure of large-scale linear algebraic equations to solve is the basis of many applications, a long time, along with the constant changes in the computing environment, the new method of the new computing environment for solving various types of large-scale linear equations adaptation quest never stopped. , Distributed memory parallel processor system has become in many scientific and engineering computing environment, the tool of choice for solving major challenges; Thus, as one of the most fundamental and most important issue in the scientific and engineering calculations - the typical structure of large-scale linear equations, the study and design of efficient parallel solution method in a distributed memory environment, it is very important theoretical and practical significance. This article is based distributed storage environment, the study of certain typical structure of large-scale linear equations parallel computing problems. Mainly to complete the work as follows: (1) study the distributed parallel solving cycle tridiagonal linear equations and proposed a parallel algorithm based on the divide-and-conquer strategy, the reduction of the equations to maintain the same structure as the original equations, and When the original equations is diagonally dominant, reduced equations remain diagonally dominant, this algorithm absolute speedup meet: (2) study of distributed parallel solving tridiagonal linear equations proposed avoid unnecessary redundant computation algorithm compared with existing algorithms further, to better balance the load between the processors, full use of overlapping technologies of computing and communications. In its absolute speedup meet: parallel efficiency to meet: (3) study the distributed parallel solving tridiagonal linear equations in Toepliz cycle decomposition, an efficient parallel algorithms based on matrix multiplication, the absolute speedup meet: theory , which is the desired result can be achieved by the parallel algorithm. (4) distributed parallel solving of the Toepliz tridiagonal equations is also based on the decomposition of the coefficient matrix, an efficient distributed parallel algorithm, the algorithm takes advantage of special structure of the coefficient matrix, to avoid the unnecessary redundancy, the absolute speedup meet: theoretically achieve the desired result of the parallel algorithm. (5) study the distributed cycle block tridiagonal linear equations are solved in parallel, to the block calculation based algorithm to achieve efficient parallel algorithms call BLAS3 subroutine, the efficiency of the algorithm has improved greatly compared with the existing algorithms. Absolute speedup meet: where s is the sub-blocks of the National Defense Science and Technology University Graduate School Dissertation Diao (6) studied the distributed parallel solving block tridiagonal linear equations to a call BLAS3 subroutine and block-based computing parallel algorithms, algorithms by solving equations workload reasonably allocated to each processor, to achieve load balancing to achieve high parallel efficiency. the absolute acceleration than meet: 1452 275 l, _,, _{<< / sub> sub> << / sub> sub>.} _{<< / sub> sub> \\}. the Hermit L _from field primary one: S ₍ n, leaves two adipic - two hundred twenty-two: n (knife related aO), where s is the inch block size. stone 5. 4 \of the Poisson equation of Dirichiet boundary conditions to export block tridiagonal linear equations obtained speedup becomes linear speedup distributed parallel algorithm, in theory, which is also the ideal parallel algorithm. (8) research triangle the distributed parallel solving of the equations, A parallel algorithm for overlapping computing and communications technology, this algorithm is faster processor computing, interprocessor communication is relatively slow, very effective. achieved than The block column scanning algorithm good results when the equations with multiple right hand side of the effect is particularly prominent. (9) distributed asymmetric large sparse linear equations solved in parallel, in the the BICG algorithm proposed amendment on the basis of, one suitable for parallel computing: BICG algorithm. BICG algorithm Lun ylov subspace iteration method in Lanczos biorthogonal method, the basic algorithm, s BICG algorithms proposed for further research Lanczos double positive The cross method like the s a steP promote lay the foundation.

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