A Preconditioned Parallel Method for Solving Large Lyapunov Matrix Equation

HOU Jun-xia; Lü Quan-yi; CAO Fang-ying; XIE Gong-nan

doi:10.3879/j.issn.1000-0887.2013.05.003

Volume 34 Issue 5

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HOU Jun-xia, Lü Quan-yi, CAO Fang-ying, XIE Gong-nan. A Preconditioned Parallel Method for Solving Large Lyapunov Matrix Equation[J]. Applied Mathematics and Mechanics, 2013, 34(5): 454-461. doi: 10.3879/j.issn.1000-0887.2013.05.003

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A Preconditioned Parallel Method for Solving Large Lyapunov Matrix Equation

doi: 10.3879/j.issn.1000-0887.2013.05.003

¹Department of Applied Mathematics, Northwestern Polytechnical University,Xi’an 710129, P.R.China;²Engineering Simulation and Aerospace Computing, School of Mechanical Engineering, Northwestern Polytechnical University,Xi’an 710072, P.R.China

Received Date: 2013-03-22
Rev Recd Date: 2013-05-03
Publish Date: 2013-05-15

Abstract

Abstract

A parallel algorithm with preconditioned modified conjugate gradient method for solving large Lyapunov matrix equation. The preconditioned Simth method for small matrix equation was first introduced, and then the modified conjugate gradient method was used for parallel solving the preconditioned Stein matrix equation, which transformed from the original Lyapunov matrix equation. To fix the involved difficulties such as the determination of the parameter μ and the solving inverse matrix of the matrix ( A +μ I ),Gerschgorin theorem and the modified conjugate gradient method were employed. Several numerical experiments show the proposed algorithm is superior to the modified conjugate gradient without precondition. The parallel efficiency is up to 0.85.
- Lypunov matrix equation,
- parallel computation,
- modified conjugate gradient method,
- precondition method

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References(8)

References

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