Some Preconditioning Iterative Algorithms for Non-Hermitian Linear Equations

ZHANG Yingchun; LI Yin; XIAO Manyu; XIE Gongnan

doi:10.21656/1000-0887.390222

Volume 40 Issue 3

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ZHANG Yingchun, LI Yin, XIAO Manyu, XIE Gongnan. Some Preconditioning Iterative Algorithms for Non-Hermitian Linear Equations[J]. Applied Mathematics and Mechanics, 2019, 40(3): 237-249. doi: 10.21656/1000-0887.390222

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Some Preconditioning Iterative Algorithms for Non-Hermitian Linear Equations

doi: 10.21656/1000-0887.390222

¹Department of Mechanical and Power Engineering, School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, P.R.China;²School of Information Technology, Shangqiu Normal University, Shangqiu, Henan 476000, P.R.China;³Department of Applied Mathematics, Northwestern Polytechnical University,Xi’an 710129, P.R.China

Funds: The National Natural Science Foundation of China(51676163)

Received Date: 2018-08-23
Rev Recd Date: 2018-09-02
Publish Date: 2019-03-01

Abstract

Abstract

Non-Hermitian linear equations have extensive application in scientific and engineering calculations and are expected to be solved with high efficiency. To accelerate the convergence rate of original algorithms, a preconditioning technique was developed and applied to some iterative methods chosen to solve the nonHermitian linear equations and complex linear systems with multiple righthand sides. Several numerical experiments show that the preconditioned iterative methods are superior to the original methods in terms of both the convergence rate and the number of iterations. In addition, the preconditioned generalized conjugate A-orthogonal residual squared method (GCORS2) has better convergent behavior and stability than other preconditioned methods.
- non-Hermitian linear equations,
- generalized conjugate A-orthogonal residual squared method,
- preconditioning method

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References

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