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HSS METHOD WITH A COMPLEX PARAMETER FOR THE SOLUTION OF COMPLEX LINEAR SYSTEM 被引量:2
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作者 Guiding Gu 《Journal of Computational Mathematics》 SCIE CSCD 2011年第4期441-457,共17页
In this paper, a complex parameter is employed in the Hermitian and skew-Hermitian splitting (HSS) method (Bai, Golub and Ng: SIAM J. Matrix Anal. Appl., 24(2003), 603-626) for solving the complex linear system... In this paper, a complex parameter is employed in the Hermitian and skew-Hermitian splitting (HSS) method (Bai, Golub and Ng: SIAM J. Matrix Anal. Appl., 24(2003), 603-626) for solving the complex linear system Ax = f. The convergence of the resulting method is proved when the spectrum of the matrix A lie in the right upper (or lower) part of the complex plane. We also derive an upper bound of the spectral radius of the HSS iteration matrix, and a estimated optimal parameter a (denoted by a^st) of this upper bound is presented. Numerical experiments on two modified model problems show that the HSS method with a est has a smaller spectral radius than that with the real parameter which minimizes the corresponding upper hound. In particular, for the 'dominant' imaginary part of the matrix A, this improvement is considerable. We also test the GMRES method preconditioned by the HSS preconditioning matrix with our parameter a est. 展开更多
关键词 Hermitian matrix Skew-Hermitian matrix Splitting iteration method complex linear system complex parameter.
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THE 2-ERROR LINEAR COMPLEXITY OF 2~n-PERIODIC BINARY SEQUENCES WITH LINEAR COMPLEXITY 2~n-1 被引量:21
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作者 Zhu Fengxiang Qi Wenfeng 《Journal of Electronics(China)》 2007年第3期390-395,共6页
Linear complexity and k-error linear complexity of the stream cipher are two important standards to scale the randomicity of keystreams. For the 2n -periodicperiodic binary sequence with linear complexity 2n 1and k = ... Linear complexity and k-error linear complexity of the stream cipher are two important standards to scale the randomicity of keystreams. For the 2n -periodicperiodic binary sequence with linear complexity 2n 1and k = 2,3,the number of sequences with given k-error linear complexity and the expected k-error linear complexity are provided. Moreover,the proportion of the sequences whose k-error linear complexity is bigger than the expected value is analyzed. 展开更多
关键词 linear complexity k-error linear complexity Periodic binary sequences Chan-Games algorithm
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Linear Complexity of Some Binary Sequences Derived from Fermat Quotients 被引量:8
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作者 Chen Zhixiong Hu Lei, Du Xiaoni 《China Communications》 SCIE CSCD 2012年第2期105-108,共4页
We determined the linear complexity of a family of p2-periodic binary threshold sequences and a family of p2-periodic binary sequences constructed using the Legendre symbol,both of which are derived from Fermat quotie... We determined the linear complexity of a family of p2-periodic binary threshold sequences and a family of p2-periodic binary sequences constructed using the Legendre symbol,both of which are derived from Fermat quotients modulo an odd prime p.If 2 is a primitive element modulo p2,the linear complexity equals to p2-p or p2-1,which is very close to the period and it is large enough for cryptographic purpose. 展开更多
关键词 CRYPTOGRAPHY pseudorandom binary sequences fermat quotients finite fields linear complexity
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ON THE LINEAR COMPLEXITY OF FCSR SEQUENCES 被引量:2
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作者 Qi Wenfeng Xu HongDept of Appl.Math,Zhengzhou Information Engineering Univ., Zhengzhou 450002,China 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2003年第3期318-324,共7页
The linear complexity of a new kind of keystream sequences.FCSR sequences,is discussed by use of the properties of cyclotomic polynomials.Based on the results of C.Seo's,an upper bound and a lower bound on the li... The linear complexity of a new kind of keystream sequences.FCSR sequences,is discussed by use of the properties of cyclotomic polynomials.Based on the results of C.Seo's,an upper bound and a lower bound on the linear complexity of a significant kind of FCSR sequences—l-sequences are presented. 展开更多
关键词 linear recurring sequence feedback with carry shift register l-sequences linear complexity
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Linear complexity of Ding generalized cyclotomic sequences 被引量:2
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作者 闫统江 陈智雄 肖国镇 《Journal of Shanghai University(English Edition)》 CAS 2007年第1期22-26,共5页
Minimal polynomials and linear complexity of binary Ding generalized cyclotomic sequences of order 2 with the two-prime residue ring Zpq are obtained by Bai in 2005. In this paper, we obtain linear complexity and mini... Minimal polynomials and linear complexity of binary Ding generalized cyclotomic sequences of order 2 with the two-prime residue ring Zpq are obtained by Bai in 2005. In this paper, we obtain linear complexity and minimal polynomials of all Ding generalized cyclotomic sequences. Our result shows that linear complexity of these sequences takes on the values pq and pq-1 on our necessary and sufficient condition with probability 1/4 and the lower bound (pq - 1)/2 with probability 1/8. This shows that most of these sequences are good. We also obtained that linear complexity and minimal polynomials of these sequences are independent of their orders. This makes it no more difficult in choosing proper p and q. 展开更多
关键词 stream cipher generalized cyclotomic sequence linear complexity minimal polynomial
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The k-Error Linear Complexity and the Linear Complexity for pq^n-Periodic Binary Sequences 被引量:1
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作者 ZHU Fengxiang QI Wenfeng 《Wuhan University Journal of Natural Sciences》 CAS 2006年第6期1549-1553,共5页
The k-error linear complexity and the linear complexity of the keystream of a stream cipher are two important standards to scale the randomness of the key stream. For a pq^n-periodic binary sequences where p, q are tw... The k-error linear complexity and the linear complexity of the keystream of a stream cipher are two important standards to scale the randomness of the key stream. For a pq^n-periodic binary sequences where p, q are two odd primes satisfying that 2 is a primitive root module p and q^2 and gcd(p-1, q-1) = 2, we analyze the relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity. 展开更多
关键词 k-error linear complexity linear complexity pq^n-periodic binary sequences
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On k-Error Linear Complexity of Some Explicit Nonlinear Pseudorandom Sequences
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作者 CHEN Zhixiong WU Chenhuang 《Wuhan University Journal of Natural Sciences》 CAS 2008年第5期577-581,共5页
Combining with the research on the linear complexity of explicit nonlinear generators of pseudorandom sequences, we study the stability on linear complexity of two classes of explicit inversive generators and two clas... Combining with the research on the linear complexity of explicit nonlinear generators of pseudorandom sequences, we study the stability on linear complexity of two classes of explicit inversive generators and two classes of explicit nonlinear generators. We present some lower bounds in theory on the k-error linear complexity of these explicit generatol's, which further improve the cryptographic properties of the corresponding number generators and provide very useful information when they are applied to cryptography. 展开更多
关键词 stream ciphers k-error linear complexity explicitinversive generators explicit nonlinear generators
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Linear Complexity of New Generalized Cyclotomic Sequences of Length 2pq
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作者 王宏伟 葛武 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2014年第6期710-716,共7页
The linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are investigated.A new generalized cyclotomic sequence Sof length 2pqis defined with an imbalance p+1.The results show ... The linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are investigated.A new generalized cyclotomic sequence Sof length 2pqis defined with an imbalance p+1.The results show that this sequence has high linear complexity. 展开更多
关键词 generalized cyclotomic sequence linear complexity minimal polynomial
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ON THE DECOMPOSITION OF COMPLEX VECTOR SPACES AND THE JORDAN CANONICAL FORM OF COMPLEX LINEAR TRANSFORMATIONS
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作者 肖衡 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第11期997-1003,共7页
New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations a... New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices. 展开更多
关键词 complex vector space complex linear transformation. decompo-sition theorems. Jordan canonical form
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THE DISTRIBUTION FUNCTIONS FOR THE LINEAR COMPLEXITY OF PERIODIC SEQUENCES
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作者 Yang Minghui Zhu Shixin 《Journal of Electronics(China)》 2012年第3期211-214,共4页
Linear complexity is an important standard to scale the randomicity of stream ciphers. The distribution function of a sequence complexity measure gives the function expression for the number of sequences with a given ... Linear complexity is an important standard to scale the randomicity of stream ciphers. The distribution function of a sequence complexity measure gives the function expression for the number of sequences with a given complexity measure value. In this paper, we mainly determine the distribution function of sequences with period over using Discrete Fourier Transform (DFT), where and the characteristics of are odd primes, gcd and is a primitive root modulo The results presented can be used to study the randomness of periodic sequences and the analysis and design of stream cipher. 展开更多
关键词 linear complexity Periodic sequences Discrete Fourier Transform (DFT)
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基于复杂网络的复杂产品系统关键节点辨识
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作者 谷晓燕 李俊 陈梦彤 《现代制造工程》 CSCD 北大核心 2024年第9期65-72,共8页
复杂产品系统具有规模大、结构复杂等特点,从系统结构的视角辨识复杂产品系统关键节点,对于“事前”定位潜在风险源具有重要意义。针对目前“事后”追溯风险源难以保证复杂产品系统可靠运行及风险管理前瞻性等问题,考虑复杂产品系统的... 复杂产品系统具有规模大、结构复杂等特点,从系统结构的视角辨识复杂产品系统关键节点,对于“事前”定位潜在风险源具有重要意义。针对目前“事后”追溯风险源难以保证复杂产品系统可靠运行及风险管理前瞻性等问题,考虑复杂产品系统的层级结构和子系统间风险的相互影响,提出了一种可用于“事前”风险管理的关键节点辨识方法。首先依据系统结构建立复杂网络;然后,构造零模型并结合网络统计特征初步划分节点集合,在此基础上引入线性阈值模型分析节点风险传播影响力,并基于风险的动态传播特征选取关键节点;最后,采用新舟700飞机的系统结构进行实证分析。结果表明,提出的方法有效地辨识了复杂产品系统的关键节点。 展开更多
关键词 复杂网络 零模型 线性阈值模型 复杂产品系统 关键节点
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ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR
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作者 陈洁玲 刘名生 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期295-310,共16页
In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,... In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors. 展开更多
关键词 Bloch-Landau type theorem Bloch constant linear complex operator harmonic mapping biharmonic mapping UNIVALENT
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高职英语教师数字胜任力现状、影响因素和个案的复杂动态分析
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作者 何中 《宁波职业技术学院学报》 2024年第5期90-101,108,共13页
基于复杂动态系统理论,采用横切面和纵深研究方法,运用统计分析、生长轨迹图和移动极值图技术,描述高职英语教师数字胜任力现状及可视化呈现其发展轨迹。研究发现:高职英语教师数字胜任力整体水平偏低,仅职称与数字胜任力部分指标存在... 基于复杂动态系统理论,采用横切面和纵深研究方法,运用统计分析、生长轨迹图和移动极值图技术,描述高职英语教师数字胜任力现状及可视化呈现其发展轨迹。研究发现:高职英语教师数字胜任力整体水平偏低,仅职称与数字胜任力部分指标存在差异性;其发展主要受个人学习因素、地方支持因素、单位环境因素、宏观政策因素影响;数字胜任力发展呈现非线性、动态性和异质性特征。研究结果拓展了复杂动态系统理论的应用边界,提出高职英语教师数字胜任力发展建议,为数字化背景下英语教师专业发展提供启示。 展开更多
关键词 复杂动态系统理论 移动极值图 纵深研究 非线性 动态性
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Statistical Characteristics of the Complexity for Prime-Periodic Sequences
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作者 NIUZhi-hua LINai-cheng XIAOGuo-zhen 《Wuhan University Journal of Natural Sciences》 EI CAS 2005年第1期211-213,共3页
Using the fact that the factorization of x^N — 1 over GF(2) is especiallyexplicit, we completely establish the distributions and the expected values of the lineal complexityand the k-error linear complexity of the N-... Using the fact that the factorization of x^N — 1 over GF(2) is especiallyexplicit, we completely establish the distributions and the expected values of the lineal complexityand the k-error linear complexity of the N-periodic sequences respectively,where N is an odd primeand 2 is a primitive root modulo N. The results show that there are a large percentage of sequenceswith both the linear complexity and the k-enor linear complexity not less than N, quite close totheir maximum possible values. 展开更多
关键词 stream ciphers periodic sequences linear complexity k-error linearcomplexity
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Equivalence of three kinds of well-posed-ness of discontinuous Riemann-Hilbert problem for elliptic complex equation in multiply connected domains
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作者 WEN Guo-chun 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第2期183-193,共11页
In this article, we first introduce the general linear elliptic complex equation of first order with certain conditions, and then propose discontinuous Riemann-Hilbert problem and some kinds of modified well-posed-nes... In this article, we first introduce the general linear elliptic complex equation of first order with certain conditions, and then propose discontinuous Riemann-Hilbert problem and some kinds of modified well-posed-ness for the complex equation. Then we verify the equivalence of three kinds of well-posed-ness. The discontinuous boundary value problem possesses many applications in mechanics and physics etc. 展开更多
关键词 Discontinuous Riemann-Hilbert problems linear elliptic complex equation equivalence of threekinds of well-posed-ness multiply connected domains.
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Pinning control of complex Lur’e networks
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作者 张庆振 李忠奎 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第6期2176-2183,共8页
This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur'e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small ... This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur'e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small fraction of the nodes. The pinning control problem is reformulated in the framework of the absolute stability theory. It is shown that the global stability of the controlled network can be reduced to the test of a set of linear matrix inequalities, which in turn guarantee the absolute stability of the corresponding Lur'e systems whose dimensions are the same as that of a single node. A circle-type criterion in the frequency domain is further presented for checking the stability of the controlled network graphically. Finally, a network of Chua's oscillators is provided as a simulation example to illustrate the effectiveness of the theoretical results. 展开更多
关键词 complex dynamical network Lur'e system pinning control linear matrix inequality
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ON STRUCTURED VARIANTS OF MODIFIED HSS ITERATION METHODS FOR COMPLEX TOEPLITZ LINEAR SYSTEMS 被引量:2
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作者 Fang Chen Yaolin Jiang Qingquan Liu 《Journal of Computational Mathematics》 SCIE CSCD 2013年第1期57-67,共11页
The Modified Hermitian and skew-Hermitian splitting (MHSS) iteration method was presented and studied by Bai, Benzi and Chen (Computing, 87(2010), 93-111) for solving a class of complex symmetric linear systems.... The Modified Hermitian and skew-Hermitian splitting (MHSS) iteration method was presented and studied by Bai, Benzi and Chen (Computing, 87(2010), 93-111) for solving a class of complex symmetric linear systems. In this paper, using the properties of Toeplitz matrix, we propose a class of structured MHSS iteration methods for solving the complex Toeplitz linear system. Theoretical analysis shows that the structured MHSS iteration method is unconditionally convergent to the exact solution. When the MHSS iteration method is used directly to complex symmetric Toeplitz linear systems, the computational costs can be considerately reduced by use of Toeplitz structure. Finally, numerical ex- periments show that the structured MHSS iteration method and the structured MHSS preconditioner are efficient for solving the complex Toeplitz linear system. 展开更多
关键词 Toeplitz matrix MHSS iteration method complex symmetric linear system.
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一类复线性系统的局部HSS迭代方法
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作者 李倩 陈键铧 《应用数学》 北大核心 2023年第1期117-125,共9页
本文提出求解一类复线性系统的局部HSS (LHSS)迭代方法.讨论迭代方法的收敛性,分析了最优迭代参数的选取.结合最优控制问题验证LHSS迭代方法的理论结果,并从迭代次数和计算时间上证明新方法的可行性和有效性.
关键词 复线性系统 对称不定矩阵 最优迭代参数 最优控制问题
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基于伪码调相线性调频复合体制测距的优化算法
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作者 刘辰 徐罗刚 +2 位作者 柯志君 徐彬杰 薛文 《微波学报》 CSCD 北大核心 2023年第S01期240-243,共4页
为了更精确快速地从复杂回波信号中提取出目标信号且使系统具备一定的抗干扰能力,提出了一种基于伪码调相线性调频复合体测距(PRBC)的优化算法——量化-二次相关法,从计算步骤和计算结构两个方面优化,更快速准确得到目标距离信息。算法... 为了更精确快速地从复杂回波信号中提取出目标信号且使系统具备一定的抗干扰能力,提出了一种基于伪码调相线性调频复合体测距(PRBC)的优化算法——量化-二次相关法,从计算步骤和计算结构两个方面优化,更快速准确得到目标距离信息。算法采用了线性调频(LFM)体制和伪码调相体制,对包含有目标的回波信号进行算法优化后的信号处理,从而得到目标的距离信息。对伪码调相线性调频复合体制雷达的回波信号进行仿真并做优化算法后的信号处理,结果表明了优化算法的有效性,从而为目标测距和干扰抑制提供了一种有价值的方案。 展开更多
关键词 伪码调相 算法优化 线性调频复合体制 信号处理
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ON CONVERGENCE PROPERTY OF THE LANCZOS METHOD FOR SOLVING A COMPLEX SHIFTED HERMITIAN LINEAR SYSTEM
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作者 Guiding Gu 《Journal of Computational Mathematics》 SCIE CSCD 2013年第3期326-334,共9页
We discuss the convergence property of the Lanczos method for solving a complex shifted Hermitian linear system (αI + H)x = f. By showing the colinear coefficient of two system's residuals, our convergence analys... We discuss the convergence property of the Lanczos method for solving a complex shifted Hermitian linear system (αI + H)x = f. By showing the colinear coefficient of two system's residuals, our convergence analysis reveals that under the condition Re(α) + λmin(H) 〉 0, the method converges faster than that for the real shifted Hermitian linear system (Re(α)I + H)x = f. Numerical experiments verify such convergence property. 展开更多
关键词 Hermitian matrix complex shifted linear system Lanczos method.
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