The Restrictively Preconditioned Conjugate Gradient Methods on Normal Residual for Block Two-by-Two Linear Systems
Year: 2008
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 2 : pp. 240–249
Abstract
The $restrictively$ $preconditioned$ $conjugate$ $gradient$ (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 $restrictively$ $preconditioned$ $conjugate$ $gradient$ $on$ $normal$ $residual$ (RPCGNR), is more robust and effective than either the known RPCG method or the standard $conjugate$ $gradient$ $on$ $normal$ $residual$ (CGNR) method when being used for solving the large sparse saddle point problems.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-JCM-8621
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 2 : pp. 240–249
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Block two-by-two linear system Saddle point problem Restrictively preconditioned conjugate gradient method Normal-residual equation Incomplete orthogonal factorization.