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Zhong-Zhi Bai

Bio: Zhong-Zhi Bai is an academic researcher from Chinese Academy of Sciences. The author has contributed to research in topics: Iterative method & System of linear equations. The author has an hindex of 49, co-authored 160 publications receiving 9600 citations. Previous affiliations of Zhong-Zhi Bai include Fudan University & Southern Federal University.


Papers
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Journal ArticleDOI
TL;DR: A class of respectively scaled Hermitian and skew-Hermitian splitting iteration method that can significantly improve the computational efficiency of the Krylov subspace iteration methods employed as effective linear solvers for the target discrete linear systems.
Abstract: Summary For the discrete linear systems resulted from the discretization of the one-dimensional anisotropic spatial fractional diffusion equations of variable coefficients with the shifted finite-difference formulas of the Grunwald–Letnikov type, we propose a class of respectively scaled Hermitian and skew-Hermitian splitting iteration method and establish its asymptotic convergence theory. The corresponding induced matrix splitting preconditioner, through further replacements of the involved Toeplitz matrices with certain circulant matrices, leads to an economic variant that can be executed by fast Fourier transforms. Both theoretical analysis and numerical implementations show that this fast respectively scaled Hermitian and skew-Hermitian splitting preconditioner can significantly improve the computational efficiency of the Krylov subspace iteration methods employed as effective linear solvers for the target discrete linear systems.

13 citations

Journal Article
TL;DR: In this article, incomplete orthogonal factorization preconditioners constructed from Givens rotations, incorporating some dropping strategies and updating tricks, for the solution of large sparse systems of linear equations are presented.
Abstract: We design, analyse and test a class of incomplete orthogonal factorization preconditioners constructed from Givens rotations, incorporating some dropping strategies and updating tricks, for the solution of large sparse systems of linear equations. Comprehensive accounts about how the preconditioners are coded, what storage is required and how the computation is executed for a given accuracy are presented. A number of numerical experiments show that these preconditioners are competitive with standard incomplete triangular factorization preconditioners when they are applied to accelerate Krylov subspace iteration methods such as GMRES and BiCGSTAB.

13 citations

Journal ArticleDOI
TL;DR: The result shows that these eigenvalues are clustered around 0 +, 2 − , and a few points located on the unit circle centered at 1, as the iteration parameter is close to 0.

13 citations

Journal ArticleDOI
TL;DR: In this article, a class of hybrid algebraic multilevel preconditioning methods for solving systems of linear equations with symmetric positive-definite matrices resulting from the discretization of many second-order elliptic boundary value problems by the finite element method is presented.

13 citations


Cited by
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Book ChapterDOI
01 Jan 2015

3,828 citations

Journal ArticleDOI
TL;DR: A large selection of solution methods for linear systems in saddle point form are presented, with an emphasis on iterative methods for large and sparse problems.
Abstract: Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.

2,253 citations

Journal ArticleDOI
TL;DR: In this article, a mathematical framework for cyber-physical systems, attacks, and monitors is proposed, and fundamental monitoring limitations from both system-theoretic and graph-based perspectives are characterized.
Abstract: Cyber-physical systems are ubiquitous in power systems, transportation networks, industrial control processes, and critical infrastructures. These systems need to operate reliably in the face of unforeseen failures and external malicious attacks. In this paper: (i) we propose a mathematical framework for cyber-physical systems, attacks, and monitors; (ii) we characterize fundamental monitoring limitations from system-theoretic and graph-theoretic perspectives; and (ii) we design centralized and distributed attack detection and identification monitors. Finally, we validate our findings through compelling examples.

1,430 citations

Posted Content
TL;DR: This paper proposes a mathematical framework for cyber-physical systems, attacks, and monitors, and describes fundamental monitoring limitations from system-theoretic and graph- theoretic perspectives and designs centralized and distributed attack detection and identification monitors.
Abstract: Cyber-physical systems integrate computation, communication, and physical capabilities to interact with the physical world and humans. Besides failures of components, cyber-physical systems are prone to malignant attacks, and specific analysis tools as well as monitoring mechanisms need to be developed to enforce system security and reliability. This paper proposes a unified framework to analyze the resilience of cyber-physical systems against attacks cast by an omniscient adversary. We model cyber-physical systems as linear descriptor systems, and attacks as exogenous unknown inputs. Despite its simplicity, our model captures various real-world cyber-physical systems, and it includes and generalizes many prototypical attacks, including stealth, (dynamic) false-data injection and replay attacks. First, we characterize fundamental limitations of static, dynamic, and active monitors for attack detection and identification. Second, we provide constructive algebraic conditions to cast undetectable and unidentifiable attacks. Third, by using the system interconnection structure, we describe graph-theoretic conditions for the existence of undetectable and unidentifiable attacks. Finally, we validate our findings through some illustrative examples with different cyber-physical systems, such as a municipal water supply network and two electrical power grids.

1,190 citations