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題名 | Palindromic Eigenvalue Problems: A Brief Survey= |
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作者 | 朱景華; 黃聰明; 林文偉; 吳金典; Chu, Eric King-wah; Huang, Tsung-ming; Lin, Wen-wei; Wu, Chin-tien; |
期刊 | Taiwanese Journal of Mathematics |
出版日期 | 20100600 |
卷期 | 14:3A 2010.06[民99.06] |
頁次 | 頁743-779 |
分類號 | 319.9 |
語文 | eng |
關鍵詞 | Crack; Crawford number; Eigenvalue; Eigenvector; Matrix polynomial; Palindromic eigenvalue problem; Train vibration; SAW filter; |
英文摘要 | The T-palindromic quadratic eigenvalue problem (λ2B +λC + A)x =0, with A, B, C ∈ Cn×n , CT =C and BT =A, governs the vibration behaviour of trains. Other palindromic eigenvalue problems, quadratic or higher order, arise from applications in surface acoustic wave filters, optimal control of discrete-time systems and crack modelling. Numerical solution of palindromic eigenvalue problems is challenging, with unacceptably low accuracy from the basic linearization approach. In this survey paper, we shall talk about the history of palindromic eigenvalue problems, in terms of their history, applications, numerical solution and generalization. We shall also speculate on some future directions of research. |
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