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

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...

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Bibliographic Details
Published in:Numerical linear algebra with applications 2018-10, Vol.25 (5), p.n/a
Main Authors: Huang, Zheng‐Da, Wang, Hui‐Di
Format: Article
Language:English
Subjects:
APIU
Convergence
Eigenvalues
GSOR
Optimization
Parameterization
Parameters
the optimal convergence factor
Uzawa
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Summary: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.
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2189