Volume 17, Issue 1
Iterative Methods with Preconditioners for Indefinite Systems

J. Comp. Math., 17 (1999), pp. 89-96.

Published online: 1999-02

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• Abstract

For the sparse linear equations $Kx=b$, where $K$ arising from optimization and discretization of some PDEs is symmetric and indefinite, it is shown that the $L \overline{L}^T$ factorization can be used to provide an "exact" preconditioner for SYMMLQ and UZAWA algorithms. "Inexact" preconditioner derived from approximate factorization is used in the numerical experiments.

• Keywords

Generalized condition number, Indefinite systems, Factorization method.

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@Article{JCM-17-89, author = {Ren , Wei-Qing and Zhao , Jin-Xi}, title = {Iterative Methods with Preconditioners for Indefinite Systems}, journal = {Journal of Computational Mathematics}, year = {1999}, volume = {17}, number = {1}, pages = {89--96}, abstract = {

For the sparse linear equations $Kx=b$, where $K$ arising from optimization and discretization of some PDEs is symmetric and indefinite, it is shown that the $L \overline{L}^T$ factorization can be used to provide an "exact" preconditioner for SYMMLQ and UZAWA algorithms. "Inexact" preconditioner derived from approximate factorization is used in the numerical experiments.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9084.html} }
TY - JOUR T1 - Iterative Methods with Preconditioners for Indefinite Systems AU - Ren , Wei-Qing AU - Zhao , Jin-Xi JO - Journal of Computational Mathematics VL - 1 SP - 89 EP - 96 PY - 1999 DA - 1999/02 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9084.html KW - Generalized condition number, Indefinite systems, Factorization method. AB -

For the sparse linear equations $Kx=b$, where $K$ arising from optimization and discretization of some PDEs is symmetric and indefinite, it is shown that the $L \overline{L}^T$ factorization can be used to provide an "exact" preconditioner for SYMMLQ and UZAWA algorithms. "Inexact" preconditioner derived from approximate factorization is used in the numerical experiments.

Wei-Qing Ren & Jin-Xi Zhao. (1970). Iterative Methods with Preconditioners for Indefinite Systems. Journal of Computational Mathematics. 17 (1). 89-96. doi:
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