ROW PROJECTION METHODS FOR LARGE NONSYMMETRIC LINEAR-SYSTEMS
ROW PROJECTION METHODS FOR LARGE NONSYMMETRIC LINEAR-SYSTEMS
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DOI：
10.1137/0913010
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发表时间：
1992-01-01
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影响因子：
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通讯作者：
SAMEH, A
中科院分区：
文献类型：
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作者：
BRAMLEY, R;SAMEH, A
介绍了非对称线性系统的三种共轭梯度加速行投影 (RP) 方法并描述了它们的特性。一种方法基于 Kaczmarz 方法，并具有作为正交投影仪乘积的迭代矩阵；另一种基于 Cimmino 的方法，并具有一个迭代矩阵，该矩阵是正交投影仪的总和。还引入了一种新的 RP 方法，该方法需要更少的矩阵向量运算，显式地减小了问题规模，在二范数中减少了误差，并且始终比其他 RP 算法产生更好的解决方案。通过与应用于正规方程的共轭梯度方法进行比较，解释了 RP 方法的属性。描述了一种行划分方法，该方法产生适用于各种计算机体系结构的并行实现，仅需要少量的额外存储向量，并且允许以较小的误差计算必要的投影。数值测试验证了该方法的稳健性，并表明所得算法在速度和效率方面与其他非对称求解器具有竞争力。
Three conjugate gradient accelerated row projection (RP) methods for nonsymmetric linear systems axe presented and their properties described. One method is based on Kaczmarz's method and has an iteration matrix that is the product of orthogonal projectors; another is based on Cimmino's method and has an iteration matrix that is the sum of orthogonal projectors. A new RP method, which requires fewer matrix-vector operations, explicitly reduces the problem size, is error reducing in the two-norm, and consistently produces better solutions than other RP algorithms, is also introduced. Using comparisons with the method of conjugate gradient applied to the normal equations, the properties of RP methods are explained.A row partitioning approach is described that yields parallel implementations suitable for a wide range of computer architectures, requires only a few vectors of extra storage, and allows computing the necessary projections with small errors. Numerical testing verifies the robustness of this approach and shows that the resulting algorithms are competitive with other nonsymmetric solvers in speed and efficiency.