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Lanczos version of bcr algorithm for solving the generalised second-order Sylvester matrix equation EVF plus GVH plus BVC = DWE plus M

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IET CONTROL THEORY AND APPLICATIONS 2017年第2期11卷 273-281页

作者： Hajarian, Masoud Shahid Beheshti Univ Fac Math Sci Dept Math Gen Campus Tehran 19839 Iran

It is well known that the biconjugate residual (bcr) algorithm and its variants are powerful procedures to find the solution of large sparse non-symmetric systems equation. In this study, the authors develop the Lanczos version of bcr algorithm for computing the solution pair of the generalised second-order Sylvester matrix equation EVF + GVH + BVC = DWE + M which includes the second-order Sylvester, Lyapunov and Stein matrix equations as special cases. The convergence results show that the algorithm with any initial matrices converges to the solutions within a finite number of iterations in the absence of round-off errors. Finally, two numerical examples are provided to support the theoretical findings and to testify the effectiveness and usefulness of the algorithm.

关键词： matrix algebra iterative methods pole assignment observers generalised second-order Sylvester matrix equation biconjugate residual algorithm Stein matrix equations Lanczos version bcr algorithm pole assignment eigenstructure assignment robust fault detection Luenberger-type observer design second-order linear system

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Efficient iterative method for generalized Sylvester quaternion tensor equation

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COMPUTATIONAL & APPLIED MATHEMATICS 2023年第5期42卷 1-26页

作者： Hu, Jingjing Ke, Yifen Ma, Changfeng Fujian Normal Univ Sch Math & Stat Fuzhou 350117 Peoples R China Fujian Normal Univ FJKLMAA Fuzhou 350117 Peoples R China Ctr Appl Math Fujian Prov FJNU Fuzhou 350117 Peoples R China

In this study, we employ the biconjugate residual (bcr) algorithm in tensor form to deal with the generalized Sylvester quaternion tensor equation in order to find the minimum norm solution. The proposed algorithm uses only tensor format. It can be proved that the proposed approach can find the solution with in a finite number of steps in the absence of round-off errors. Furthermore, we can get the unique minimal Frobenius norm solution by choosing special kinds of initial tensor. Finally, some numerical examples are reported to illustrate the feasibility of our algorithm, including the effectiveness of the algorithm in color video restoration problems.

关键词： Quaternion tensor Sylvester tensor equation bcr algorithm Color video restoration

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bcr method for solving generalized coupled Sylvester equations over centrosymmetric or anti-centrosymmetric matrix

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2018年第1期75卷 70-88页

作者： Lv, Chang-Qing Ma, Chang-Feng Fujian Normal Univ Coll Math & Informat Fujian Key Lab Math Anal & Applicat Fuzhou 350117 Fujian Peoples R China Zaozhuang Univ Sch Math & Stat Zaozhuang 277160 Peoples R China

This paper introduces another version of biconjugate residual method (bcr) for solving the generalized coupled Sylvester matrix equations over centrosymmetric or anti-centrosymmetric matrix. We prove this version of bcr algorithm can find the centrosymmetric solution group of the generalized coupled matrix equations for any initial matrix group within finite steps in the absence of round-off errors. Furthermore, a method is provided for choosing the initial matrices to obtain the least norm solution of the problem. At last, some numerical examples are provided to illustrate the efficiency and validity of methods we have proposed. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Generalized coupled Sylvester equations bcr algorithm Centrosymmetric (anti-centrosymmetric) matrix Convergence Numerical experiment

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Matrix form of Biconjugate Residual algorithm to Solve the Discrete-Time Periodic Sylvester Matrix Equations

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ASIAN JOURNAL OF CONTROL 2018年第1期20卷 49-56页

作者： Hajarian, Masoud Shahid Beheshti Univ Fac Math Sci Dept Math Gen Campus Tehran 19839 Iran

There are important relationships between the discrete-time linear periodic descriptor systems and the discrete-time periodic matrix equations. In the present paper, we introduce the matrix form of the biconjugate residual (bcr) algorithm for solving the discrete-time periodic Sylvester matrix equations A(i)X(i)B(i)+CiXi+1Di=E-i,i=1,2,.... It is shown that the introduced algorithm converges to the solutions within a finite number of iterations in the absence of round-off errors. Finally, three numerical examples are given to demonstrate the efficiency and the performance of the algorithm.

关键词： bcr algorithm Sylvester discrete-time periodic matrix equation Lyapunov discrete-time periodic matrix equation

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Local Tb Theorem on Spaces of Homogeneous Type

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ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN 2009年第3期28卷 333-347页

作者： Tan, Chaoqiang Yan, Lixin Shantou Univ Dept Math Shantou 515063 Guangdong Peoples R China Zhongshan Univ Dept Math Guangzhou 510275 Guangdong Peoples R China

In this article, we obtain a local Tb theorem for singular integral operators on spaces of homogeneous type by using tree selection algorithm of the dyadic model and the bcr algorithm, which extends an earlier result ... 详细信息

关键词： Local Tb theorem singular integral operators trees bcr algorithm spaces of homogeneous type

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Wavelet decomposition of Calderon-Zygmund operators on function spaces

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JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY 2004年第1期77卷 29-46页

作者： Lau, KS Yan, LX Chinese Univ Hong Kong Dept Math Shatin Hong Kong Peoples R China Zhongshan Univ Dept Math Guangzhou 510275 Peoples R China

We make use of the Beylkin-Coifman-Rokhlin wavelet decomposition algorithm on the Calderon-Zygmund kernel to obtain some fine estimates on the operator and prove the T(1) theorem on Besov and Triebel-Lizorkin spaces. ... 详细信息

关键词： Calderon-Zygmund operator Besov space Triebel-Lizorkin space wavelet bcr algorithm

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L² boundedness of commutators of Calderon-Zygmund singular integral operators

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PROGRESS IN NATURAL SCIENCE 1998年第4期8卷 416-427页

作者： Deng, DG Yan, LX Yang, QX Zhongshan Univ Dept Math Canton 510275 Peoples R China

L-2 boundedness of commutators of Calderon-Zygmund singular integral operators with weak kernel [b, T]f = bTf - T(bf) is proved when b is an element of BMO. This result extends Coifman-Rochberg-Weiss Theorem. An equivalent version is that bilinear operator gT(f) - fT* (g) is an element of H-1, provided f, g is an element of L-2. This is a new result in the compensated compactness theory.

关键词： commutator singular integral BMO Hardy space wavelets bcr algorithm

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