论文信息 - A note on block-diagonally preconditioned PIU methods for singular saddle point problems

A note on block-diagonally preconditioned PIU methods for singular saddle point problems

Recently, Bai and Wang [On parameterized inexact Uzawa methods for generalized saddle point problems, Linear Algebra Appl. 428 (2008), pp. 2900–2932] and Gao and Kong [Block diagonally preconditioned PIU methods of saddle point problems, Appl. Math. Comput. 216 (2010), pp. 1880–1887] discussed the parameterized inexact Uzawa (PIU) method and the preconditioned parameterized inexact Uzawa (PPIU) method. In this paper, we further study the block-diagonally preconditioned PIU methods for solving singular saddle point problems, and give the corresponding convergence analysis.

Haifeng Ma | Naimin Zhang | Naimin Zhang | Haifeng Ma

[1] X. Wu,et al. Conjugate Gradient Method for Rank Deficient Saddle Point Problems , 2004, Numerical Algorithms.

[2] Louis A. Hageman,et al. Iterative Solution of Large Linear Systems. , 1971 .

[3] A. Wathen,et al. Minimum residual methods for augmented systems , 1998 .

[4] Ning Gao,et al. Block diagonally preconditioned PIU methods of saddle point problem , 2010, Appl. Math. Comput..

[5] Zhi-Hao Cao,et al. On the convergence of iterative methods for solving singular linear systems , 2002 .

[6] Zeng-Qi Wang,et al. On parameterized inexact Uzawa methods for generalized saddle point problems , 2008 .

[7] Gene H. Golub,et al. Numerical solution of saddle point problems , 2005, Acta Numerica.

[8] John J. H. Miller. On the Location of Zeros of Certain Classes of Polynomials with Applications to Numerical Analysis , 1971 .

[9] Bing Zheng,et al. On semi-convergence of parameterized Uzawa methods for singular saddle point problems☆ , 2009 .

[10] Beresford N. Parlett,et al. On generalized successive overrelaxation methods for augmented linear systems , 2005, Numerische Mathematik.