预处理变形共轭梯度法并行求解矩阵的Moore-Penrose逆

A parallel preconditioned modified conjugate gradient method of Moore-Penrose inverse of matrices

提出了一种求解Moore-Penrose逆的并行预处理变形共轭梯度法,将求解Moore-Penrose逆转化求解矩阵方程极小范数解或极小范数最小二乘解的问题.给出了两种预处理方法.一种方法是给出预处理矩阵是可逆对角矩阵,然后并行求解预处理矩阵方程;另一种方法是给出预处理矩阵是严格对角占优矩阵,该方法提出了迭代法的预处理模式,构造并行迭代求解预处理矩阵方程的迭代格式,进而使用变形共轭梯度法并行求解.通过数值试验,这两种预处理方法与直接使用变形共轭梯度法相比较,第二种方法有效提高了收敛速度,而且具有很好的并行性.

A solution is presented about parallel preconditioned modified conjugate gradient method of solving Moore-Penrose inverse of matrices, and the Moore-Penrose inverse transformation in solving the matrix equation for minimum norm solution or minimal norm least squares solution problem. It gives two kinds of preconditioned methods in this paper. One method gives that the preconditioned matrix is invertible diagonal matrix, and then parallel solving pretreatment matrix equation; the other is that the preconditioned matrix is strictly diagonally dominant matrix, and the method proposes preconditioned model of iterative method, structures iterative format of parallel iteratire algorithm for preconditioned matrix equation, and then use the modified conjugate gradient method for parallel solution. Through numerical experiments, comparing the two pretreated methods and the direct use of deformation of the modified conjugate gradient method, the second method promotes the effectiveness,and has good parallelism.