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Volume 6, Issue 3
A Block Diagonal Preconditioner for Generalised Saddle Point Problems

Zhong Zheng & Guo Feng Zhang

DOI: 10.4208/eajam.260815.280216a

East Asian J. Appl. Math., 6 (2016), pp. 235-252.

Published online: 2018-02

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  • Abstract

A lopsided alternating direction iteration (LADI) method and an induced block diagonal preconditioner for solving block two-by-two generalised saddle point problems are presented. The convergence of the LADI method is analysed, and the block diagonal preconditioner can accelerate the convergence rates of Krylov subspace iteration methods such as GMRES. Our new preconditioned method only requires a solver for two linear equation sub-systems with symmetric and positive definite coefficient matrices. Numerical experiments show that the GMRES with the new preconditioner is quite effective.

  • Keywords

Generalised saddle point problem, Krylov subspace methods, alternating direction iteration, preconditioning, convergence.

  • AMS Subject Headings

15A06, 65F10, 65H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-6-235, author = {Zhong Zheng and Guo Feng Zhang}, title = {A Block Diagonal Preconditioner for Generalised Saddle Point Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {6}, number = {3}, pages = {235--252}, abstract = {

A lopsided alternating direction iteration (LADI) method and an induced block diagonal preconditioner for solving block two-by-two generalised saddle point problems are presented. The convergence of the LADI method is analysed, and the block diagonal preconditioner can accelerate the convergence rates of Krylov subspace iteration methods such as GMRES. Our new preconditioned method only requires a solver for two linear equation sub-systems with symmetric and positive definite coefficient matrices. Numerical experiments show that the GMRES with the new preconditioner is quite effective.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.260815.280216a}, url = {http://global-sci.org/intro/article_detail/eajam/10795.html} }
TY - JOUR T1 - A Block Diagonal Preconditioner for Generalised Saddle Point Problems AU - Zhong Zheng & Guo Feng Zhang JO - East Asian Journal on Applied Mathematics VL - 3 SP - 235 EP - 252 PY - 2018 DA - 2018/02 SN - 6 DO - http://doi.org/10.4208/eajam.260815.280216a UR - https://global-sci.org/intro/article_detail/eajam/10795.html KW - Generalised saddle point problem, Krylov subspace methods, alternating direction iteration, preconditioning, convergence. AB -

A lopsided alternating direction iteration (LADI) method and an induced block diagonal preconditioner for solving block two-by-two generalised saddle point problems are presented. The convergence of the LADI method is analysed, and the block diagonal preconditioner can accelerate the convergence rates of Krylov subspace iteration methods such as GMRES. Our new preconditioned method only requires a solver for two linear equation sub-systems with symmetric and positive definite coefficient matrices. Numerical experiments show that the GMRES with the new preconditioner is quite effective.

Zhong Zheng and Guo Feng Zhang. (2018). A Block Diagonal Preconditioner for Generalised Saddle Point Problems. East Asian Journal on Applied Mathematics. 6 (3). 235-252. doi:10.4208/eajam.260815.280216a
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