System theory for numerical analysis
System theory for numerical analysis
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DOI：
10.1016/j.automatica.2006.12.028
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发表时间：
2007-07
期刊：
影响因子：
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通讯作者：
K. Kashima;Y. Yamamoto
中科院分区：
文献类型：
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作者：
K. Kashima;Y. Yamamoto
许多数值方案可以从系统理论的角度进行适当的研究。本文研究了数值分析与系统论这两门学科之间的关系。我们首先看到，线性和非线性方程的各种迭代求解方案可以适当地转化为闭环反馈系统的形式，并显示在这种情况下的内模原理的关键作用。这导致了新的稳定性标准牛顿的方法。然后，我们研究了求解微分方程的Runge-Kutta类型方法，并根据线性矩阵不等式的最新结果推导了新的稳定性准则。最后给出了一个数值例子来说明本文理论的优越性。
Many numerical schemes can be suitably studied from a system theoretic point of view. This paper studies the relationship between the two disciplines, that is, numerical analysis and system theory. We first see that various iterative solution schemes for linear and nonlinear equations can be suitably transformed into the form of a closed-loop feedback system, and show the crucial role of the internal model principle in such a context. This leads to new stability criteria for Newton's method. We then study Runge–Kutta type methods for solving differential equations, and also derive new stability criteria based on recent results on LMI. A numerical example is given to illustrate the advantage of the present theory.