CAO Fang-ying, Lü Quan-yi, XIE Gong-nan. A Parallel Preconditioned Modified Conjugate Gradient Method for a Kind of Matrix Equation[J]. Applied Mathematics and Mechanics, 2013, 34(3): 240-251. doi: 10.3879/j.issn.1000-0887.2013.03.004
Citation: CAO Fang-ying, Lü Quan-yi, XIE Gong-nan. A Parallel Preconditioned Modified Conjugate Gradient Method for a Kind of Matrix Equation[J]. Applied Mathematics and Mechanics, 2013, 34(3): 240-251. doi: 10.3879/j.issn.1000-0887.2013.03.004

A Parallel Preconditioned Modified Conjugate Gradient Method for a Kind of Matrix Equation

doi: 10.3879/j.issn.1000-0887.2013.03.004
  • Received Date: 2013-01-29
  • Rev Recd Date: 2013-03-01
  • Publish Date: 2013-03-15
  • In view of a parallel algorithm of preconditioned modified conjugate gradient method for solving a kind of matrix equationAXB=C,a preconditioned model was proposed. Based on this thought, firstly the preconditioned matrix was constructed, which was strictly diagonally dominant matrix, secondly the parallel algorithm for preprocessing matrix equation iterative format was formed, and finally the modified conjugate gradient method was used for parallel solving the preconditioned matrix equation. Through numerical experiments, comparing our algorithm with the modified conjugate gradient method, ours has higher parallel efficiency.
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