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The AOR-Base Splitting Modified Fixed Point Iteration for Solving Absolute Value Equations
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作者 Changfeng Ma Jing Kang 《Communications in Mathematical Research》 CSCD 2024年第3期261-274,共14页
Recently,Yu et al.presented a modified fixed point iterative(MFPI)method for solving large sparse absolute value equation(AVE).In this paper,we consider using accelerated overrelaxation(AOR)splitting to develop the mo... Recently,Yu et al.presented a modified fixed point iterative(MFPI)method for solving large sparse absolute value equation(AVE).In this paper,we consider using accelerated overrelaxation(AOR)splitting to develop the modified fixed point iteration(denoted by MFPI-JS and MFPI-GSS)methods for solving AVE.Furthermore,the convergence analysis of the MFPI-JS and MFPI-GSS methods for AVE are also studied under suitable restrictions on the iteration parameters,and the functional equation between the parameter T and matrix Q.Finally,numerical examples show that the MFPI-JS and MFPI-GSS are efficient iteration methods. 展开更多
关键词 absolute value equation modified point iteration convergence analysis numerical experiment
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A Novel Inverse-Free Neurodynamic Approach for Solving Absolute Value Equations
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作者 Tao Li 《Journal of Applied Mathematics and Physics》 2024年第10期3458-3468,共11页
We propose a novel inverse-free neurodynamic approach (NIFNA) for solving absolute value equations (AVE). The NIFNA guarantees global convergence and notably improves convergence speed by achieving fixed-time converge... We propose a novel inverse-free neurodynamic approach (NIFNA) for solving absolute value equations (AVE). The NIFNA guarantees global convergence and notably improves convergence speed by achieving fixed-time convergence. To validate the theoretical findings, numerical simulations are conducted, demonstrating the effectiveness and efficiency of the proposed NIFNA. 展开更多
关键词 absolute value equations Neurodynamic Approach Fixed-Time Convergence Numerical Simulations
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Concave Minimization for Sparse Solutions of Absolute Value Equations 被引量:5
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作者 刘晓红 樊婕 李文娟 《Transactions of Tianjin University》 EI CAS 2016年第1期89-94,共6页
Based on concave function, the problem of finding the sparse solution of absolute value equations is relaxed to a concave programming, and its corresponding algorithm is proposed, whose main part is solving a series o... Based on concave function, the problem of finding the sparse solution of absolute value equations is relaxed to a concave programming, and its corresponding algorithm is proposed, whose main part is solving a series of linear programming. It is proved that a sparse solution can be found under the assumption that the connected matrixes have range space property(RSP). Numerical experiments are also conducted to verify the efficiency of the proposed algorithm. 展开更多
关键词 absolute value equations concave minimization SPARSITY linear programming range space property
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A New Fixed-Time Dynamical Systemfor Absolute Value Equations
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作者 Xuehua Li Dongmei Yu +2 位作者 Yinong Yang Deren Han Cairong Chen 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2023年第3期622-633,共12页
A novel dynamical model with fixed-time convergence is presented to solve the system of absolute value equations(AVEs).Under a mild condition,it is proved that the solution of the proposed dynamical system converges t... A novel dynamical model with fixed-time convergence is presented to solve the system of absolute value equations(AVEs).Under a mild condition,it is proved that the solution of the proposed dynamical system converges to the solution of the AVEs.Moreover,in contrast to the existing inversion-free dynamical system(C.Chen et al.,Appl.Numer.Math.168(2021),170–181),a conservative settling-time of the proposed method is given.Numerical simulations illustrate the effectiveness of the new method. 展开更多
关键词 absolute value equation fixed-time convergence dynamical system numerical simulation
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Tensor absolute value equations 被引量:10
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作者 Shouqiang Du Liping Zhang +1 位作者 Chiyu Chen Liqun Qi 《Science China Mathematics》 SCIE CSCD 2018年第9期1695-1710,共16页
This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems ... This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems and is a generalization of the well-known absolute value equations in the matrix case. We prove that tensor absolute value equations are equivalent to some special structured tensor complementary problems. Some sufficient conditions are given to guarantee the existence of solutions for tensor absolute value equations. We also propose a Levenberg-Marquardt-type algorithm for solving some given tensor absolute value equations and preliminary numerical results are reported to indicate the efficiency of the proposed algorithm. 展开更多
关键词 M-tensors absolute value equations Levenberg-Marquardt method tensor complementarity problem
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Further study on tensor absolute value equations 被引量:3
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作者 Chen Ling Weijie Yan +1 位作者 Hongjin He Liqun Qi 《Science China Mathematics》 SCIE CSCD 2020年第10期2137-2156,共20页
In this paper,we consider the tensor absolute value equations(TAVEs),which is a newly introduced problem in the context of multilinear systems.Although the system of the TAVEs is an interesting generalization of matri... In this paper,we consider the tensor absolute value equations(TAVEs),which is a newly introduced problem in the context of multilinear systems.Although the system of the TAVEs is an interesting generalization of matrix absolute value equations(AVEs),the well-developed theory and algorithms for the AVEs are not directly applicable to the TAVEs due to the nonlinearity(or multilinearity)of the problem under consideration.Therefore,we first study the solutions existence of some classes of the TAVEs with the help of degree theory,in addition to showing,by fixed point theory,that the system of the TAVEs has at least one solution under some checkable conditions.Then,we give a bound of solutions of the TAVEs for some special cases.To find a solution to the TAVEs,we employ the generalized Newton method and report some preliminary results. 展开更多
关键词 tensor absolute value equations H^+-tensor P-tensor copositive tensor generalized Newton method
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The Sparsest Solution to the System of Absolute Value Equations 被引量:3
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作者 Min Zhang Zheng-Hai Huang Yu-Fan Li 《Journal of the Operations Research Society of China》 EI CSCD 2015年第1期31-51,共21页
On one hand,to find the sparsest solution to the system of linear equations has been a major focus since it has a large number of applications in many areas;and on the other hand,the system of absolute value equations... On one hand,to find the sparsest solution to the system of linear equations has been a major focus since it has a large number of applications in many areas;and on the other hand,the system of absolute value equations(AVEs)has attracted a lot of attention since many practical problems can be equivalently transformed as a system of AVEs.Motivated by the development of these two aspects,we consider the problem to find the sparsest solution to the system of AVEs in this paper.We first propose the model of the concerned problem,i.e.,to find the solution to the system of AVEs with the minimum l0-norm.Since l0-norm is difficult to handle,we relax the problem into a convex optimization problem and discuss the necessary and sufficient conditions to guarantee the existence of the unique solution to the convex relaxation problem.Then,we prove that under such conditions the unique solution to the convex relaxation is exactly the sparsest solution to the system of AVEs.When the concerned system of AVEs reduces to the system of linear equations,the obtained results reduce to those given in the literature.The theoretical results obtained in this paper provide an important basis for designing numerical method to find the sparsest solution to the system of AVEs. 展开更多
关键词 absolute value equations The sparsest solution Minimum l1-norm solution
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