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On the optimal convergence factor of the accelerated parameterized inexact Uzawa method with three parameters for augmented systems
Author(s) -
Huang ZhengDa,
Wang HuiDi
Publication year - 2018
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2189
Subject(s) - mathematics , parameterized complexity , convergence (economics) , eigenvalues and eigenvectors , schur complement , complement (music) , factor (programming language) , mathematical optimization , algorithm , computer science , biochemistry , physics , chemistry , quantum mechanics , complementation , programming language , economics , gene , phenotype , economic growth
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.