| 计算对称带状矩阵广义特征值问题的并行分治多分法 |
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| 引用本文： | 魏立峰,李晓梅.计算对称带状矩阵广义特征值问题的并行分治多分法[J].高等学校计算数学学报,2003,25(3):205-210. |
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| 作者姓名： | 魏立峰 李晓梅 |
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| 作者单位： | 国防科技大学计算机学院计算机研究所,长沙,410073 |
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| 摘 要： | 1 引 言 本文研究了广义特征值问题 Ax=λBx (1)的并行计算。其中,A,B均为半带宽为r的n阶实对称带状矩阵且其中之一是正定的.本文总假设B是正定的.
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| 关 键 词： | 对称带状矩阵 广义特征值问题 并行分治多分法 特征值重构 复杂性 广义Rayleigh商迭代 |
| 修稿时间： | 2001年6月18日 |
PARALLEL DIVIDE AND CONQUER ALGORITHM WITH MULTISECTION FOR REAL SYMMETRIC BAND GENERALIZED EIGENVALUE PROBLEM |
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| Wei Lifeng Li Xiaomei.PARALLEL DIVIDE AND CONQUER ALGORITHM WITH MULTISECTION FOR REAL SYMMETRIC BAND GENERALIZED EIGENVALUE PROBLEM[J].Numerical Mathematics A Journal of Chinese Universities,2003,25(3):205-210. |
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| Authors: | Wei Lifeng Li Xiaomei |
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| Abstract: | In this paper we present a parallel divide and conquer algorithm combined with multisection for solving the generalized eigenproblem of real symmetric band matrices under distributing environment. This algorithm computes generalized eigenpaires of symmetric band matrix pencil by divide and conquer combined with multisection and generalized Rayleigh quotient iteration. Proved by theoretic analysis and numerical experiments, this algorithm is better than the classic algorithm DSBGVX in LAPACK when the scale of matrices is large enough. During parallel computing, there are little communications between processors. So high speedup can be expected. |
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| Keywords: | generalized eigenvalue problem symmetric band matrices divide and conquer generalized Rayleigh quotient iteration |
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