本文選題：半純函數(shù)　切入點：廣義幅值原理　出處：《浙江工商大學》2017年碩士論文　論文類型：學位論文

【摘要】：本文研究了利用廣義幅值原理來解決半純函數(shù)零極點的問題。為了使理論的敘述更加清晰,易于理解,理論體系更加完善,我們首先介紹了半純函數(shù)的基本理論和性質(zhì),并且在此基礎(chǔ)上,利用復平面上半純函數(shù)的基本性質(zhì),推導出廣義幅值原理.而后我們展示了如何應(yīng)用它來為一些半純函數(shù)的定理給出簡單的證明,這部分內(nèi)容一方面是為了說明廣義幅值原理的重要性,另一方面我們也為后文應(yīng)用它來解決半純函數(shù)的零極點問題,給出有用的定理。我們重點介紹了用廣義幅值原理求解半純函數(shù)零極點的基本原理,這一部分承上啟下,它基于廣義幅值原理,同時為后文的算法提供理論基礎(chǔ)。在此基礎(chǔ)上,我們給出了兩種利用廣義幅值原理求解半純函數(shù)零點的算法和誤差分析。最后我們用具體的實例來說明如何應(yīng)用之前給出的算法來解決半純函數(shù)的零極點問題,以及應(yīng)用算法時的注意事項。
[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.
【學位授予單位】：浙江工商大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O174.52

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1 方小珂;利用廣義幅值原理求解半純函數(shù)的零點及極點[D];浙江工商大學;2017年

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本文編號：1652415