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| 1 | Further study on tensor absolute value equations显示文摘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. | Chen Ling Weijie Yan Hongjin He Liqun Qi | 2020 | Science China Mathematics2020，63，10： | 2 |
| 2 | 改进的正弦余弦算法求解广义绝对值方程的最小一范数解显示文摘针对存在多个解的广义绝对值方程,定义了智能算法的适应值函数,研究了正弦余弦算法中控制参数的特征,给出了一个改进的正弦余弦算法,最后应用于寻找广义绝对值方程的最小一范数解. | 雍龙泉 贾伟 黎延海 | 2021 | 海南大学学报(自然科学版)2021，39，1： | 1 |
| 3 | The Generalized Order Tensor Complementarity Problems显示文摘The main propose of this paper is devoted to study the solvability of the generalized order tensor complementarity problem.We define two problems:the generalized order tensor complementarity problem and the vertical tensor comple-mentarity problem and show that the former is equivalent to the latter.Using the degree theory,we present a comprehensive analysis of existence,uniqueness and stability of the solution set of a given generalized order tensor complementarity problem. | Maolin Che Liqun Qi Yimin Wei | 2020 | Numerical Mathematics(Theory,Methods and Applications)2020，13，1： | 1 |
| 4 | On Nonnegative Solution of Multi-Linear System with Strong M_(z)-Tensors显示文摘A class of structured multi-linear system defined by strong M_(z)-tensors is considered.We prove that the multi-linear system with strong M_(z)-tensors always has a nonnegative solution under certain condition by the fixed point theory.We also prove that the zero solution is the only solution of the homogeneous multi-linear system for some structured tensors,such as strong M-tensors,H^(+)-tensors,strictly diagonally dominant tensors with positive diagonal elements.Numerical examples are presented to illustrate our theoretical results. | Changxin Mo Yimin Wei | 2021 | Numerical Mathematics(Theory,Methods and Applications)2021，14，1： | 0 |
| 5 | 张量空间上的仿射变分不等式显示文摘本文考虑张量空间上的变分不等式并讨论一些基本性质.特别地,借助一类张量乘积,定义一类张量空间上的仿射变分不等式,讨论这类变分不等式解集的性质,包括解的存在唯一性和解集的有界性.最后考察一类寡头垄断市场博弈问题,将其建模为一个张量空间上的仿射变分不等式,为此类问题的进一步研究提供动力. | 李夏 黄正海 | 2022 | 中国科学:数学2022，52，3： | 0 |
| 6 | 求解张量绝对值方程的非精确LM方法显示文摘通过引入互补函数将张量绝对值问题重新表述为张量互补问题.针对重构的张量互补问题,建立了自适应非精确LM算法,并证明了算法的收敛性.数值实验结果表明所提出的算法是有效的. | 马昌凤 谢亚君 | 2023 | 河南师范大学学报(自然科学版)2023，51，1： | 0 |
| 7 | 求解广义张量绝对值方程的光滑化牛顿算法显示文摘本文提出了一种求解广义张量绝对值方程的光滑化牛顿算法.广义张量绝对值方程是对矩阵广义绝对值方程的推广,目前得到了广泛的关注.我们证明了在一种弱且容易验证的条件下,光滑牛顿算法是有全局收敛性的,同时我们给出了数值实验来说明算法的有效性. | 郭旭 谷伟哲 | 2020 | 数学进展2020，49，6： | 0 |
| 8 | 求解张量互补问题的一类光滑模系矩阵迭代方法显示文摘本文提出了求解张量互补问题的一类光滑模系矩阵迭代方法.其基本思想是,先将张量互补问题转化为等价的模系方程组,然后引入一个逼近的光滑函数进行求解.我们分析了算法的收敛性,并通过数值实验验证了所提出算法的有效性. | 宋珊珊 李郴良 | 2022 | 计算数学2022，44，2： | 0 |
| 9 | 求解M-张量方程的两种新型算法显示文摘多重线性系统在当今的工程计算和数据挖掘等领域有很多实际应用,许多问题可以转化为多重线性系统求解问题.在本文中,我们首先提出了一种新的迭代算法来求解系数张量为M-张量的多重线性系统,在此基础上又提出了一种新的改进算法,并对两种算法的收敛性进行了分析.数值算例的结果表明,本文提出的两种算法是有效的并且改进算法的迭代时间更少. | 邵新慧 祁猛 | 2022 | 计算数学2022，44，2： | 0 |
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