| A REGULARIZED CONJUGATE GRADIENT METHOD FOR SYMMETRIC POSITIVE DEFINITE SYSTEM OF LINEAR EQUATIONS |
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| 作者姓名： | Zhong-zhi Bai |
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| 作者单位： | Zhong-zhi Bai(LSEC，ICMSEC，Academy of Mathematics and System Sciences，Chinese Academy of Sciences，Beijing 100080，China)Shao-liang Zhang(Department of Applied Physics，University of Tokyo，7-3-1 Hongo，Bunkyo-ku，Tokyo 113-8656，Japan) |
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| 基金项目： | Subsidized by The Special Funds For Major State Basic Research Projects G1999032803. |
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| 摘 要： | AbstractA class of regularized conjugate gradient methods is presented for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned symmetric positive definite matrix. The convergence properties of these methods are discussed in depth, and the best possible choices of the parameters involved in the new methods are investigated in detail. Numerical computations show that the new methods are more efficient and robust than both classical relaxation methods and classical conjugate direction methods.
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A REGULARIZED CONJUGATE GRADIENT METHOD FOR SYMMETRIC POSITIVE DEFINITE SYSTEM OF LINEAR EQUATIONS |
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| Zhong-zhi Bai.A REGULARIZED CONJUGATE GRADIENT METHOD FOR SYMMETRIC POSITIVE DEFINITE SYSTEM OF LINEAR EQUATIONS[J].Journal of Computational Mathematics,2002(4). |
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| Authors: | Zhong-zhi Bai |
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| Abstract: | A class of regularized conjugate gradient methods is presented for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned symmetric positive definite matrix. The convergence properties of these methods are discussed in depth, and the best possible choices of the parameters involved in the new methods are investigated in detail. Numerical computations show that the new methods are more efficient and robust than both classical relaxation methods and classical conjugate direction methods. |
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| Keywords: | Conjugate gradient method Symmetric positive definite matrix Regulariza-tion Ill-conditioned linear system |
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