標題: 在二次特徵值問題中對QR迭代法的平行方法
A Parallel Method for the Double-Shift QR Iteration in the Quadratic Eigenvalue Problem
作者: 蔡□杰
Heng-Chieh Tsai
林朝枝
Chau-Jy Lin
應用數學系所
關鍵字: 平行方法;QR迭代法;Parallel Method;Double-Shift QR Iteration
公開日期: 2001
摘要: 在這篇論文中,我們學習二次特徵值問題 ( A + B + C)x = 0 的數值解,其中A、B、C是n維的實矩陣且A是可逆矩陣。首先將二次特徵值問題轉換成較大的標準的特徵值問題 其中 是一個維度2n的矩陣。然後應用Householder轉換與QR迭代法去取得 矩陣的特徵值。為了在迭代的過程中能更快地得到特徵值,我們提供一個對QR迭代法的平行方法。這個對QR迭代法的平行方法在資料傳輸方面我們減少了約三分之二的資料傳輸時間。
In this paper, we study the numerical solution of the quadratic eigenvalue problem ( A + B + C)x = 0, where A, B, and C are real nxn matrices, and A is nonsingular. We transform the quadratic eigenvalue problem into an enlarged standard eigenvalue problem where is a matrix of order 2n. Then we apply the Householder method and the double-shift QR iteration to get the eigenvalues of matrix . In order to obtain the eigenvalues faster, we propose a parallel method for the double-shift QR iteration. Our parallel method for the double-shift QR iteration decreases data-transferring time to one-third.
URI: http://140.113.39.130/cdrfb3/record/nctu/#NT900507006
http://hdl.handle.net/11536/69300
Appears in Collections:Thesis