Wen Ruiping, Duan Hui
Higher Education Key Laboratory of Engineering and Scientific Computing, Taiyuan Normal University, Taiyuan, Shanxi 030012 P.R. China.
Department of Mathematics, Taiyuan Normal University, Taiyuan, Shanxi 030012 P.R. China.
J Inequal Appl. 2017;2017(1):95. doi: 10.1186/s13660-017-1370-7. Epub 2017 May 1.
In this paper, a parallel multisplitting iterative method with the self-adaptive weighting matrices is presented for the linear system of equations when the coefficient matrix is an -matrix. The zero pattern in weighting matrices is determined in advance, while the non-zero entries of weighting matrices are determined by finding the optimal solution in a hyperplane of points generated by the parallel multisplitting iterations. Especially, the nonnegative restriction of weighting matrices is released. The convergence theory is established for the parallel multisplitting method with self-adaptive weightings. Finally, a numerical example shows that the parallel multisplitting iterative method with the self-adaptive weighting matrices is effective.
本文针对系数矩阵为 -矩阵的线性方程组，提出了一种具有自适应加权矩阵的并行多分裂迭代方法。加权矩阵的零模式预先确定，而加权矩阵的非零元素通过在由并行多分裂迭代生成的 个点的超平面中找到最优解来确定。特别地，放宽了加权矩阵的非负限制。建立了具有自适应加权的并行多分裂方法的收敛理论。最后，一个数值例子表明具有自适应加权矩阵的并行多分裂迭代方法是有效的。
