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iterative algorithms for solving the matrix equation AXB+CX^TD = E

APPLIED MATHEMATICS AND COMPUTATION 2007年第2期187卷 622-629页

作者： Wang, Minghui Cheng, Xuehan Wei, Musheng E China Normal Univ Dept Math Shanghai 200062 Peoples R China Qufu Normal Univ Dept Math Qufu 273165 Peoples R China

In this paper, we propose two iterative algorithms to solve the matrix equation AXB + (CXD)-D-T = E. The first algorithm is applied when the matrix equation is consistent. In this case, for any (special) initial matrix X-1, a solution (the minimal Frobenius norm solution) can be obtained within finite iteration steps in the absence of roundoff errors. The second algorithm is applied when the matrix equation is inconsistent. In this case, for any (special) initial matrix X-1, a least squares solution (the minimal Frobenius norm least squares solution) can be obtained within finite iteration steps in the absence of roundoff errors. Some examples verify the efficiency of these algorithms. (c) 2006 Elsevier Inc. All rights reserved.

关键词： iterative algorithm Kronecker product conjugate gradient method matrix equation

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iterative algorithms for a new class of extended general nonconvex set-valued variational inequalities

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2010年第12期73卷 3907-3923页

作者： Alimohammady, M. Balooee, J. Cho, Y. J. Roohi, M. Gyeongsang Natl Univ Dept Math Educ Chinju 660701 South Korea Gyeongsang Natl Univ RINS Chinju 660701 South Korea Univ Mazandaran Dept Math Fac Basic Sci Babol Sar 474161468 Iran

Some new classes of extended general nonconvex set-valued variational inequalities and the extended general Wiener-Hopf inclusions are introduced. By the projection technique, equivalence between the extended general nonconvex set-valued variational inequalities and the fixed point problems as well as the extended general nonconvex Wiener-Hopf inclusions is proved. Then by using this equivalent formulation, we discuss the existence of solutions of the extended general nonconvex set-valued variational inequalities and construct some new perturbed finite step projection iterative algorithms with mixed errors for approximating the solutions of the extended general nonconvex set-valued variational inequalities. We also verify that the approximate solutions obtained by our algorithms converge to the solutions of the extended general nonconvex set-valued variational inequalities. The results presented in this paper extend and improve some known results from the literature. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Variational inequalities Wiener-Hopf inclusions iterative algorithm Monotone operators Prox-regularity Convergence analysis

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iterative algorithms for a System of Variational Inclusions Involving Set-Valued Quasi-Contractive Mappings in Banach Spaces

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2021年第8期42卷 865-882页

作者： Qiu, Yangqing Liu, Xiaomei Shanghai Polytech Univ Dept Math Shanghai 201209 Peoples R China

In this paper, a new system of variational inclusions involving set-valued quasi-contractive, lower semi-continuous mappings with nonempty closed and convex values is introduced and studied in real Banach spaces. First, both the existence of fixed points of the set-valued quasi-contractive mappings and the solution of the system of variational inclusions are proved. Then, using the existence result, a new iterative algorithm is constructed. And then the strong convergence of the iterative sequences is proved, and the proof is novel. Finally, a numerical example is given to demonstrate the algorithm. Our results improve and extend some known results.

关键词： Convergence fixed point iterative algorithm quasi-contractive mapping system of variational inclusions

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iterative algorithms for partitioned neural network approximation to partial differential equations

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2024年 170卷 237-259页

作者： Yang, Hee Jun Kim, Hyea Hyun Kyung Hee Univ Dept Appl Math Yongin South Korea Kyung Hee Univ Inst Nat Sci Yongin South Korea

To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network defined on the whole problem domain. In such a partitioned neural network approach, suitable interface conditions or subdomain boundary conditions are combined to obtain a convergent approximate solution. However, there has been no rigorous study on the convergence and parallel computing enhancement on the partitioned neural network approach. In this paper, iterative algorithms are proposed to enhance parallel computation performance in the partitioned neural network approximation. Our iterative algorithms are based on classical additive Schwarz domain decomposition methods. For the proposed iterative algorithms, their convergence is analyzed under an error assumption on the local and coarse neural network solutions. Numerical results are also included to show the performance of the proposed iterative algorithms.

关键词： Partitioned neural network approximation Partial differential equation iterative algorithm Domain decomposition Parallel computing

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iterative algorithms for attitude estimation using global positioning system phase measurements

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2001年第5期24卷 983-990页

作者： Nadler, A Bar-Itzhack, IY Weiss, H Technion Israel Inst Technol Fac Aerosp Engn IL-32000 Haifa Israel

algorithms are sought for attitude determination using global positioning system (GPS) differential phase measurements, assuming that the cycle integer ambiguities are known. The problem of attitude determination is posed as a constrained parameter optimization problem, where a quaternion-based quartic cost function is used. A new general minimization scheme is developed. The new scheme is a continuous version of the well-known Newton-Raphson algorithm and is based on the solution of an ordinary differential equation. The new continuous algorithm converges exponentially from any initial condition to the closest local minimum located on the gradient direction in regions where the associated Hessian matrix is positive definite. Three new algorithms are developed for solving the attitude estimation problem, a discrete Newton-Raphson-based algorithm, a continuous Newton-Raphson algorithm, and an algorithm that is based on the eigenproblem structure of the nonlinear equations, which are related to the minimization of the quartic cost function. The performance of the new algorithms is evaluated via numerical examples and compared with each other and against the well-known QUEST algorithm. The continuous Newton-Raphson algorithm and the eigenproblem algorithm have similar accuracy. The discrete Newton-Raphson algorithm is less efficient than the continuous Newton-Raphson algorithm in the examined minimization because its search may wander and may even reach a nonrelevant extreme. When the GPS satellites are at low elevation, the accuracy of the new algorithms is better than that of QUEST, when the latter is applied to vectorized phase measurements.

关键词： GPS iterative algorithm Quaternions GPS Satellites Nonlinear Equation Satellites Earth Yaw Euler Angles Cartesian Coordinate System

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iterative algorithms for a new system of nonlinear variational inclusions with (A, η)-accretive mappings in Banach spaces

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2007年第4期54卷 579-588页

作者： Jin, Mao-Ming Fuling Normal Univ Dept Math Chongqing 408003 Peoples R China

In this paper we introduce and study a new system of nonlinear variational inclusions with (A, eta)-accretive mappings in Banach spaces. By using the resolvent operator associated with (A, eta)-accretive mappings, we construct some new iterative algorithms for approximating the solution of this system of variational inclusions. We also prove the existence of solutions and the convergence of the sequences generated by the algorithm in Banach spaces. The results presented in this paper extend and improve some known results in the literature. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： (A, eta)-accretive mapping system of nonlinear variational inclusions resolvent operator technique iterative algorithm convergence

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iterative algorithms for the input and state recovery from the approximate inverse of strictly proper multivariable systems

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2018年 101卷 320-337页

作者： Chen, Liwen Xu, Qiang Lamar Univ Dan F Smith Dept Chem Engn POB 10053 Beaumont TX 77710 USA

This paper proposes new iterative algorithms for the unknown input and state recovery from the system outputs using an approximate inverse of the strictly proper linear time invariant (LTI) multivariable system. One of the unique advantages from previous system inverse algorithms is that the output differentiation is not required. The approximate system inverse is stable due to the systematic optimal design of a dummy feedthrough D matrix in the state-space model via the feedback stabilization. The optimal design procedure avoids trial and error to identify such a D matrix which saves tremendous amount of efforts. From the derived and proved convergence criteria, such an optimal D matrix also guarantees the convergence of algorithms. Illustrative examples show significant improvement of the reference input signal tracking by the algorithms and optimal D design over non-iterative counterparts on controllable or stabilizable LTI systems, respectively. Case studies of two Boeing-767 aircraft aerodynamic models further demonstrate the capability of the proposed methods. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Approximate inverse Dummy D matrix iterative algorithm Stability Strictly proper

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iterative algorithms for solving inverse problems of heat conduction in multiply connected domains

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2012年第4期55卷 744-751页

作者： Frackowiak, A. Cialkowski, M. Wroblewska, A. Poznan Univ Tech Chair Thermal Engn PL-60965 Poznan Poland

The presented paper displays a method of solving the inverse problems of heat transfer in multi-connected regions, consisting in iterative solving of convergent series of the direct problems. For known temperature and flux values at the outer boundary of the region the temperature and flux values at the inner boundaries are sought (the cauchy problem for the Laplace equation). In case of such a formulation of the problem, the solution does not always exist, one of the conditions is met in the mean-square sense, providing the optimization criterion. The idea of the process consists in solving the direct problem in which the boundary condition is subject to iterative changes so as to attain minimum of the optimization criterion (the square functional). Two algorithms have been formulated. In the first of them the heat flux at the inner boundaries of the region, while in the other the temperature were subject to changes. Convergence of both the algorithms have been compared. The numerical calculation has been made for selected examples, for which an analytical solution is known. The effect of random disturbance of the boundary conditions on the solution obtained with iterative algorithms has been checked. Moreover, a function was defined, serving as convergence measure of the solution of the inverse problem solved with the algorithms proposed in the paper. The properties of the function give evidence that it tends to the value exceeding unity. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Inverse problem Cauchy problem iterative algorithm

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iterative algorithms with variable anchors for non-expansive mappings

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2008年第1-2期28卷 39-49页

作者： Yao, Yonghong Zhou, Haiyun Liou, Yeong-Cheng Tianjin Polytech Univ Dept Math Tianjin 300160 Peoples R China Shijiazhuang Mech Engn Coll Dept Math Shijiazhuang 050003 Peoples R China Cheng Shiu Univ Dept Informat Management Kaohsiung 833 Taiwan

In this paper, we suggest and analyze some new iterative algorithms with variable anchors for non-expansive mapping in Banach spaces. We prove that the proposed iterative algorithms converge strongly to a fixed point of some non-expansive mapping. We also obtain some corollaries which include some results as special cases. Furthermore, we conclude the strong convergence of the so-called viscosity iterative algorithms.

关键词： Non-expansive mapping iterative algorithm Fixed point Strong convergence

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iterative algorithms for improving consistency of intuitionistic preference relations

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2014年第5期65卷 708-722页

作者： Xu, Z. Xia, M. PLA Univ Sci & Technol Nanjing 210007 Jiangsu Peoples R China Tsinghua Univ Beijing 100084 Peoples R China

Consistency of preference relations is an important research topic in decision making with preference information. The existing research about consistency mainly focuses on multiplicative preference relations, fuzzy preference relations and linguistic preference relations. Intuitionistic preference relations, each of their elements is composed of a membership degree, a non-membership degree and a hesitation degree, can better reflect the very imprecision of preferences of decision makers. There has been little research on consistency of intuitionistic preference relations up to now, and thus, it is necessary to pay attention to this issue. In this paper, we first propose an approach to constructing the consistent (or approximate consistent) intuitionistic preference relation from any intuitionistic preference relation. Then we develop a convergent iterative algorithm to improve the consistency of an intuitionistic preference relation. Moreover, we investigate the consistency of intuitionistic preference relations in group decision making situations, and show that if all individual intuitionistic preference relations are consistent, then the collective intuitionistic preference relation is also consistent. Moreover, we develop a convergent iterative algorithm to improve the consistency of all individual intuitionistic preference relations. The practicability and effectiveness of the developed algorithms is verified through two examples.

关键词： group decision making intuitionistic preference relation consistency iterative algorithm

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