Author
Zhong-Zhi Bai
Other affiliations: Fudan University, Southern Federal University, Shanghai University of Science and Technology ...read more
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 published on a yearly basis
Papers
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TL;DR: A class of asynchronous parallel nonlinear multisplitting relaxation methods for solving system of nonlinear equations with special choices of the relaxed parameters is established.
Abstract: In this paper, we establish a class of asynchronous parallel nonlinear multisplitting relaxation methods for solving system of nonlinear equations. With special choices of the relaxed parameters in the new methods, not only can the convergence properties of them be improved, but also many applicable and efficient asynchronous parallel nonlinear multisplitting iteration methods such as the Jacobi, Gauss-Seidel, SOR as well as the asynchronous parallel nonlinear multisplitting AOR-Newton, -Chord and -Steffensen programs, etc., can be obtained. Under proper conditions, we build convergence theories about these asynchronous methods, and estimate their asymptotic convergence rates in detailed manner.
7 citations
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TL;DR: The localQ-superlinear convergence of the algorithm is proved without introducing anm-step refactorization and the numerical results of the new algorithm are compared with those of the known algorithms, implying that the new algorithms is satisfactory.
Abstract: In this paper, we establish a class of sparse update algorithm based on matrix triangular factorizations for solving a system of sparse equations. The localQ-superlinear convergence of the algorithm is proved without introducing anm-step refactorization. We compare the numerical results of the new algorithm with those of the known algorithms, The comparison implies that the new algorithm is satisfactory.
6 citations
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TL;DR: A class of multi-parameter relaxed parallel matrix multisplitting methods for solving the linear complementarity problems on the SIMD multiprocessor systems under the condition that the system matrix is an H-matrix with positive diagonal elements.
Abstract: We set up a class of multi-parameter relaxed parallel matrix multisplitting methods for solving the linear complementarity problems on the SIMD multiprocessor systems. This class of methods can not only includes all the existing relaxed methods for the linear complementarity problems, but also can yields a lot of novel ones in the sense of multisplitting. Thus, it is reasonably general. We set up the convergence theory of these relaxed methods under the condition that the system matrix is an H-matrix with positive diagonal elements.
6 citations
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TL;DR: Theoretical analysis shows that not only do these new methods lend themselves to parallel computation, but also their convergence rates are independent of both the sizes and the level numbers of the grids, and their computational work loads are also bounded by linear functions of the step sizes of the finest grids.
6 citations
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TL;DR: Asynchronous parallel multisplitting nonlinear iterative methods are established for the system of nonlinear algebraic equations in this paper, with A, T ∈ L ( R n ) being matrices having particular properties, ϕ, ψ : R n → R n being diagonal and continuous mappings, and b ∈ R n a known vector.
Abstract: Asynchronous parallel multisplitting nonlinear iterative methods are established for the system of nonlinear algebraic equations Aϕ ( x ) + Tψ ( x ) = b , with A , T ∈ L ( R n ) being matrices having particular properties, ϕ , ψ : R n → R n being diagonal and continuous mappings, and b ∈ R n a known vector, and their global convergence and asymptotic convergence rates are investigated in detail under some reasonable conditions.
5 citations
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01 Jan 20153,828 citations
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2,618 citations
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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
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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
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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