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Volume 20, Issue 4
A Regularized Conjugate Gradient Method for Symmetric Positive Definite System of Linear Equations

Zhong-Zhi Bai & Shao-Liang Zhang

J. Comp. Math., 20 (2002), pp. 437-448.

Published online: 2002-08

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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 invoved 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.

  • Keywords

Conjugate gradient method, Symmetric positive definite matrix, Regularization, Ill-conditioned linear system.

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COPYRIGHT: © Global Science Press

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@Article{JCM-20-437, author = {Bai , Zhong-Zhi and , Shao-Liang Zhang}, title = {A Regularized Conjugate Gradient Method for Symmetric Positive Definite System of Linear Equations}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {4}, pages = {437--448}, 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 invoved 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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8930.html} }
TY - JOUR T1 - A Regularized Conjugate Gradient Method for Symmetric Positive Definite System of Linear Equations AU - Bai , Zhong-Zhi AU - , Shao-Liang Zhang JO - Journal of Computational Mathematics VL - 4 SP - 437 EP - 448 PY - 2002 DA - 2002/08 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8930.html KW - Conjugate gradient method, Symmetric positive definite matrix, Regularization, Ill-conditioned linear system. AB -

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 invoved 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.

Bai , Zhong-Zhi and , Shao-Liang Zhang. (2002). A Regularized Conjugate Gradient Method for Symmetric Positive Definite System of Linear Equations. Journal of Computational Mathematics. 20 (4). 437-448. doi:
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