保結構迴紋式二次化求解迴紋式方程

Abstract

本文探討的主題是開發和利用高效率迴紋二次化的方法來解決結構迴紋多項式特徵值的問題。第1章將簡要介紹一些基本概念，數學符號和一般所謂的『迴紋多項式特徵值問題』。在第2章中，起源於德國的高速列車之計算與振動分析和表面聲波濾波器的研究，我們探討和分析高效率的方法去解決多項式特徵值問題。在第3章中，我們將提出一個保結構解決方法去對付奇次的迴紋矩陣多項式以及展示明確的遞迴係數矩陣。最後，這篇論文的結論和未來的工作將在第4章討論。

The theme explored in this thesis is to develop and exploit efficient palindromic quadratization methods to solve the structure-palindromic polynomial eigenvalue problem. This chapter will briefly introduce some basic notions, mathematical notations and conventional methods of the so-called “palindromic polynomial eigenvalue problems”. In Chapter 2, we investigate and analyze efficient methods for polynomial eigenvalue problems arising from computing in the vibration analysis for fast trains in Germany and then in the study of surface acoustic wave filters. In Chapter 3, we will propose a structured-preserving method of palindromic matrix polynomial of odd degree and show the explicitly recursive coefficient matrices. Finally, conclusions and the future work of this thesis will be discussed in Chapter 4.