Volume 26, Issue 2
The Restrictively Preconditioned Conjugate Gradient Methods on Normal Residual for Block

Junfeng Yin & Zhongzhi Bai

DOI:

J. Comp. Math., 26 (2008), pp. 240-249

Published online: 2008-04

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  • Abstract

The {\em restrictively preconditioned conjugate gradient} (RPCG) method is further developed to solve large sparse system of linear equations of a block two-by-two structure. The basic idea of this new approach is that we apply the RPCG method to the normal-residual equation of the block two-by-two linear system and construct each required approximate matrix by making use of the incomplete orthogonal factorization of the involved matrix blocks. Numerical experiments show that the new method, called the {\em restrictively preconditioned conjugate gradient on normal residual} (RPCGNR), is more robust and effective than either the known RPCG method or the standard {\em conjugate gradient on normal residual} (CGNR) method when being used for solving the large sparse saddle point problems.

  • Keywords

Block two-by-two linear system Saddle point problem Restrictively preconditioned conjugate gradient method Normal-residual equation Incomplete orthogonal factorization

  • AMS Subject Headings

65F10 65W05.

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COPYRIGHT: © Global Science Press

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@Article{JCM-26-240, author = {}, title = {The Restrictively Preconditioned Conjugate Gradient Methods on Normal Residual for Block}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {2}, pages = {240--249}, abstract = { The {\em restrictively preconditioned conjugate gradient} (RPCG) method is further developed to solve large sparse system of linear equations of a block two-by-two structure. The basic idea of this new approach is that we apply the RPCG method to the normal-residual equation of the block two-by-two linear system and construct each required approximate matrix by making use of the incomplete orthogonal factorization of the involved matrix blocks. Numerical experiments show that the new method, called the {\em restrictively preconditioned conjugate gradient on normal residual} (RPCGNR), is more robust and effective than either the known RPCG method or the standard {\em conjugate gradient on normal residual} (CGNR) method when being used for solving the large sparse saddle point problems.}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8621.html} }
TY - JOUR T1 - The Restrictively Preconditioned Conjugate Gradient Methods on Normal Residual for Block JO - Journal of Computational Mathematics VL - 2 SP - 240 EP - 249 PY - 2008 DA - 2008/04 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8621.html KW - Block two-by-two linear system KW - Saddle point problem KW - Restrictively preconditioned conjugate gradient method KW - Normal-residual equation KW - Incomplete orthogonal factorization AB - The {\em restrictively preconditioned conjugate gradient} (RPCG) method is further developed to solve large sparse system of linear equations of a block two-by-two structure. The basic idea of this new approach is that we apply the RPCG method to the normal-residual equation of the block two-by-two linear system and construct each required approximate matrix by making use of the incomplete orthogonal factorization of the involved matrix blocks. Numerical experiments show that the new method, called the {\em restrictively preconditioned conjugate gradient on normal residual} (RPCGNR), is more robust and effective than either the known RPCG method or the standard {\em conjugate gradient on normal residual} (CGNR) method when being used for solving the large sparse saddle point problems.
Junfeng Yin & Zhongzhi Bai. (1970). The Restrictively Preconditioned Conjugate Gradient Methods on Normal Residual for Block. Journal of Computational Mathematics. 26 (2). 240-249. doi:
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