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    数学与统计学院2024年第5期学术论坛

    发布时间:2024-04-23 浏览量:

    会议时间:2024年4月24日(周三)14:30-16:00

    会议地点:线上腾讯会议:170-328-368

    报告1:Modified conjugate direction algorithm for solving the 3-order general coupled tensor equations over symmetric tensors

    报告人:吕长青

    内容简介:Symmetric solutions of the linear tensor equations have wide applications in the finite element, finite difference, spectral method, mechanical or electrical engineering. In this paper, a modified conjugate direction algorithm (MCD) is proposed for solving generalized coupled Sylvester tensor equations. It’s proved that this algorithm can obtain the solution of the tensor equations for any initial tensor group within finite steps in the absence of round-off errors. Furthermore, a method is provided for choosing the initial tensors 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.

    报告2:高阶随机非线性系统的自适应状态反馈镇定

    报告人:秦孝艳

    内容简介:本文针对一类高阶随机不确定非线性系统,其漂移项与扩散项依赖于所有状态,研究了此系统的自适应状态反馈镇定问题.通过选取恰当的Lyapunov 函数,利用自适应

    增加幂积分方法、反推技术、参数分离原理和一些代数技巧设计参数,构造了一个光滑自适应控制器.所设计的控制器能保证闭环系统对任意初始值几乎处处存在惟一解,平衡点依概率全局稳定并且系统的状态几乎处处调节到零.仿真例子验证了控制方案的有效性.

    报告3:A new efficient one-step method for the highly precise solution of the one-dimensional Schr\"{o}dinger equation

    报告人:刘石威

    内容简介:In this talk, a new efficient one-step method is constructed for the highly precise solution of the one-dimensional Schr\"{o}dinger equation. This method is based on a new family of power series methods which can be easily extended to arbitrary order. The error analysis indicates that the new method will have good numerical performance especially for large eigenvalues. The stability and phase properties are examined. Numerical results confirm this analysis and demonstrate that our new method is superior over some high-quality Runge-kutta-type methods recently proposed in the literature in accuracy and efficiency.

    科技处

    2024年4月24日

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