利用广义幅值原理求解半纯函数的零点及极点

发布时间：2018-03-23 07:11

本文选题：半纯函数　切入点：广义幅值原理　出处：《浙江工商大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文研究了利用广义幅值原理来解决半纯函数零极点的问题。为了使理论的叙述更加清晰,易于理解,理论体系更加完善,我们首先介绍了半纯函数的基本理论和性质,并且在此基础上,利用复平面上半纯函数的基本性质,推导出广义幅值原理.而后我们展示了如何应用它来为一些半纯函数的定理给出简单的证明,这部分内容一方面是为了说明广义幅值原理的重要性,另一方面我们也为后文应用它来解决半纯函数的零极点问题,给出有用的定理。我们重点介绍了用广义幅值原理求解半纯函数零极点的基本原理,这一部分承上启下,它基于广义幅值原理,同时为后文的算法提供理论基础。在此基础上,我们给出了两种利用广义幅值原理求解半纯函数零点的算法和误差分析。最后我们用具体的实例来说明如何应用之前给出的算法来解决半纯函数的零极点问题,以及应用算法时的注意事项。
[Abstract]:In this paper, the generalized amplitude principle is used to solve the problem of zero and pole point of hemisomorphic function. In order to make the description of the theory more clear, easy to understand and perfect, we first introduce the basic theory and properties of the semi-pure function. On this basis, the generalized amplitude principle is derived by using the basic properties of the semipure function on the complex plane, and then we show how to use it to give a simple proof for the theorems of some semi-pure functions. On the one hand, this part is to illustrate the importance of the generalized amplitude principle, on the other hand, we also apply it to solve the zero pole problem of the semi-pure function. Some useful theorems are given. We mainly introduce the basic principle of using generalized amplitude principle to solve the zero and pole point of semi-pure function. This part is based on the generalized amplitude principle and provides a theoretical basis for the following algorithms. In this paper, we give two algorithms and error analysis to solve the zero point of a semi-pure function by using the generalized amplitude principle. Finally, we use a concrete example to illustrate how to solve the zero pole problem of a semi-pure function by using the algorithm given before. And the application of the algorithm matters needing attention.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O174.52

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