Two-parameter GSOR method for the augmented system

Li, Zheng; Li, Changjun; Evans, David; Zhang, Tie

doi:10.1080/00207160500112860

Cited by 12 publications

(9 citation statements)

References 7 publications

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“…Therefore, it is necessary to find the simplification of formula (4) or an appropriate estimate of ) det(W .…”

Section: Resultsmentioning

confidence: 99%

A Note on the Eigenvalues of Saddle Point Matrices

Zhang

2008

2008 International Conference on Intelligent Computation Technology and Automation (ICICTA)

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The spectral properties of saddle point matrices arising from saddle point problems are discussed. The relations of the eigenvalues and the determinants between the saddle point matrices and their sub blocks are investigated. An appropriate estimate on the maximum eigenvalue of saddle point matrix is given. In the numerical experiment the saddle point matrices derived from the mixed finite element discretizations on Stokes equation are observed. Numerical results confirm the theoretical analysis and demonstrate that the estimate on the maximum eigenvalue of saddle point matrix is proper.

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“…Therefore, it is necessary to find the simplification of formula (4) or an appropriate estimate of ) det(W .…”

Section: Resultsmentioning

confidence: 99%

A Note on the Eigenvalues of Saddle Point Matrices

Zhang

2008

2008 International Conference on Intelligent Computation Technology and Automation (ICICTA)

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“…Equations (41) and (42) imply (38), which proves that the first part holds. When ≤ − 1 u , we obtain by (24), (30), and the first part, that the modulus of 12…”

Section: Lemmamentioning

confidence: 91%

“…If functions

f, sans-serifg, h

satisfy

h false(α false) = f false(α false) sans-serifg false(α false), α \in D_{f, sans-serifg, h},

then becomes the method in the GSOR‐like family that is defined in the work of Huang and Zhou . Clearly, the methods that are defined in other works are special members of this family with the special choice of functions

f, sans-serifg, h

. Here, we only list functions for methods in other works, which are not included in the work of Huang and Zhou …”

Section: Variants Of the Apiu Methodsmentioning

confidence: 99%

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On the optimal convergence factor of the accelerated parameterized inexact Uzawa method with three parameters for augmented systems

Huang

Wang

2018

Numerical Linear Algebra App

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Summary Under the assumption that all eigenvalues of the preconditioned Schur complement are real, we present an analytical proof for obtaining the optimal convergence factor of the real accelerated parameterized inexact Uzawa (APIU) method when P=A. It is proved that the optimal convergence factor is the same as that of the generalized successive overrelaxation method, which was published at the same time, and that it can be attained only at the unique optimum point of parameters, regardless of whether m>n or m=n. In addition, we generalize the APIU method and analyze the relationship between the APIU method and 10 additional Uzawa‐like methods.

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“…For its property of large and sparsity, system (1.1) is suitable for being solved by the iterative methods. There are many efficient iterative methods have been studied in the literature, see [2][3][4][5][6][7][8][9][10]. Recently, Golub et al [2] proposed the SOR-like method and considered the optimum choice for iterative parameter.…”

Section: Introductionmentioning

confidence: 99%