The Parameterized Augmentation Block Preconditioner for Nonsymmetric Saddle Point Problems

doi:10.1007/s42967-024-00383-0

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (5): 1704-1723.doi: 10.1007/s42967-024-00383-0

• ORIGINAL PAPERS • 上一篇

The Parameterized Augmentation Block Preconditioner for Nonsymmetric Saddle Point Problems

Bo Wu

School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, Ningxia, China

收稿日期:2023-10-26 修回日期:2024-02-06 接受日期:2024-02-07 出版日期:2024-06-22 发布日期:2024-06-22
通讯作者: Bo Wu,E-mail:wubo@nxu.edu.cn E-mail:wubo@nxu.edu.cn

The Parameterized Augmentation Block Preconditioner for Nonsymmetric Saddle Point Problems

Bo Wu

School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, Ningxia, China

Received:2023-10-26 Revised:2024-02-06 Accepted:2024-02-07 Online:2024-06-22 Published:2024-06-22
Contact: Bo Wu,E-mail:wubo@nxu.edu.cn E-mail:wubo@nxu.edu.cn

摘要/Abstract

摘要： Based on the preconditioner presented by He and Huang (Comput Math Appl 62: 87–92, 2011), we introduce a parameterized augmentation block preconditioner for solving the nonsymmetric saddle point problems with the singular (1,1)-block. The theoretical analysis gives the eigenvalue and eigenvector properties of the corresponding preconditioned matrix, and numerical results confirm the effectiveness of the preconditioner for accelerating the convergence rate of the generalized minimal residual (GMRES) method when solving the large sparse nonsymmetric saddle point problems.

关键词: Augmentation, Preconditioner, Eigenvalue property, Generalized minimal residual (GMRES)

Abstract: Based on the preconditioner presented by He and Huang (Comput Math Appl 62: 87–92, 2011), we introduce a parameterized augmentation block preconditioner for solving the nonsymmetric saddle point problems with the singular (1,1)-block. The theoretical analysis gives the eigenvalue and eigenvector properties of the corresponding preconditioned matrix, and numerical results confirm the effectiveness of the preconditioner for accelerating the convergence rate of the generalized minimal residual (GMRES) method when solving the large sparse nonsymmetric saddle point problems.

Key words: Augmentation, Preconditioner, Eigenvalue property, Generalized minimal residual (GMRES)

Bo Wu. The Parameterized Augmentation Block Preconditioner for Nonsymmetric Saddle Point Problems[J]. Communications on Applied Mathematics and Computation, 2025, 7(5): 1704-1723.

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The Parameterized Augmentation Block Preconditioner for Nonsymmetric Saddle Point Problems

The Parameterized Augmentation Block Preconditioner for Nonsymmetric Saddle Point Problems

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