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移位QR算則在三對角矩陣上之收斂 / Convergence of the Shifted QR Algorithm on Tridiagonal Matrices

在計算矩陣的特徵值(eigenvalues)中,QR演算法是一種常見的技巧. 尤其如果使用適當的移位,將可以較快得到特徵值. 在本文中提出一種新的移位策略, 我們證明這各方法是可行的,而且可適用於任何矩陣. 換句說, 本篇論文主旨即是提出有關新的移位QR演算法的收斂. / The QR algorithm is a popular method for computing all the
eigenvalues of a dense matrix. If we use a proper shift, we can
accelerate convergence of the iterative process. Hence, we design a new shift strategy which includes an eigenvalue of the trailing principal 3-by-3 submatrix of the tridiagonal matrix. We prove the global convergence of the new strategy. In other words, the purpose of this thesis is to propose a theory of the convergence of a new shifted QR algorithm.

Identiferoai:union.ndltd.org:CHENGCHI/G0090751008
Creators蔡淑芬, Tsai ,Shu-Fen
Publisher國立政治大學
Source SetsNational Chengchi University Libraries
Language英文
Detected LanguageEnglish
Typetext
RightsCopyright © nccu library on behalf of the copyright holders

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