This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obt...This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.展开更多
The solution of linear equation group can be applied to the oil exploration, the structure vibration analysis, the computational fluid dynamics, and other fields. When we make the in-depth analysis of some large or ve...The solution of linear equation group can be applied to the oil exploration, the structure vibration analysis, the computational fluid dynamics, and other fields. When we make the in-depth analysis of some large or very large complicated structures, we must use the parallel algorithm with the aid of high-performance computers to solve complex problems. This paper introduces the implementation process having the parallel with sparse linear equations from the perspective of sparse linear equation group.展开更多
This paper proposes a parallel algorithm, called KDOP (K-DimensionalOptimal Parallel algorithm), to solve a general class of recurrence equations efficiently. The KDOP algorithm partitions the computation into a serie...This paper proposes a parallel algorithm, called KDOP (K-DimensionalOptimal Parallel algorithm), to solve a general class of recurrence equations efficiently. The KDOP algorithm partitions the computation into a series of sub-computations, each of which is executed in the fashion that all the processors work simultaneously with each one executing an optimal sequential algorithm to solve a subcomputation task. The algorithm solves the equations in O(N/p)steps in EREW PRAM model (Exclusive Read Exclusive Write Parallel Ran-dom Access Machine model) using p<N1-e processors, where N is the size of the problem, and e is a given constant. This is an optimal algorithm (itsspeedup is O(p)) in the case of p<N1-e. Such an optimal speedup for this problem was previously achieved only in the case of p<N0.5. The algorithm can be implemented on machines with multiple processing elements or pipelined vector machines with parallel memory systems.展开更多
针对基于PVM的桌面PC机联网而成的网络并行计算环境中，处理机的运算速度较快，而处理机间的通信相对较慢的实际情况，提出了求解线性方程组的一种分组Guass-Seidel并行迭代算法，该算法将线性方程组的增广矩阵按行分块储存在各处理机...针对基于PVM的桌面PC机联网而成的网络并行计算环境中，处理机的运算速度较快，而处理机间的通信相对较慢的实际情况，提出了求解线性方程组的一种分组Guass-Seidel并行迭代算法，该算法将线性方程组的增广矩阵按行分块储存在各处理机，每台处理机分别对各自的块采用Guass-Seidel迭代法进行迭代计算，其处理机间的通信较少，实现容易。并用1～24台桌面PC机联成的局域网，在PVM 3．4 on Windows2000，VC 6．0并行计算平台上编程对该算法进行了数值试验，试验结果表明，该算法较传统的Jacobi并行迭代算法和传统的Guass—Seidel并行迭代算法更优越。展开更多
基金This project is supported by the National Natural Science Foundation of China
文摘This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.
文摘The solution of linear equation group can be applied to the oil exploration, the structure vibration analysis, the computational fluid dynamics, and other fields. When we make the in-depth analysis of some large or very large complicated structures, we must use the parallel algorithm with the aid of high-performance computers to solve complex problems. This paper introduces the implementation process having the parallel with sparse linear equations from the perspective of sparse linear equation group.
文摘This paper proposes a parallel algorithm, called KDOP (K-DimensionalOptimal Parallel algorithm), to solve a general class of recurrence equations efficiently. The KDOP algorithm partitions the computation into a series of sub-computations, each of which is executed in the fashion that all the processors work simultaneously with each one executing an optimal sequential algorithm to solve a subcomputation task. The algorithm solves the equations in O(N/p)steps in EREW PRAM model (Exclusive Read Exclusive Write Parallel Ran-dom Access Machine model) using p<N1-e processors, where N is the size of the problem, and e is a given constant. This is an optimal algorithm (itsspeedup is O(p)) in the case of p<N1-e. Such an optimal speedup for this problem was previously achieved only in the case of p<N0.5. The algorithm can be implemented on machines with multiple processing elements or pipelined vector machines with parallel memory systems.
文摘针对基于PVM的桌面PC机联网而成的网络并行计算环境中，处理机的运算速度较快，而处理机间的通信相对较慢的实际情况，提出了求解线性方程组的一种分组Guass-Seidel并行迭代算法，该算法将线性方程组的增广矩阵按行分块储存在各处理机，每台处理机分别对各自的块采用Guass-Seidel迭代法进行迭代计算，其处理机间的通信较少，实现容易。并用1～24台桌面PC机联成的局域网，在PVM 3．4 on Windows2000，VC 6．0并行计算平台上编程对该算法进行了数值试验，试验结果表明，该算法较传统的Jacobi并行迭代算法和传统的Guass—Seidel并行迭代算法更优越。
