CIRR: a Rayleigh-Ritz type method with contour integral for generalized eigenvalue problems
CIRR: a Rayleigh-Ritz type method with contour integral for generalized eigenvalue problems
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DOI：
10.14492/hokmj/1272848031
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发表时间：
2007-11
影响因子：
0.5
通讯作者：
T. Sakurai;Hiroto Tadano
中科院分区：
文献类型：
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作者：
T. Sakurai;Hiroto Tadano
本文考虑一种Rayleigh-Ritz型特征值求解器，用于求解广义特征值问题在一定区域内的有限特征值及其相应的特征向量。当矩阵非常大时，使用迭代方法来生成包含所需特征向量的不变子空间。近似是从子空间通过瑞利-里兹投影的。本文提出了一种带围道积分的Rayleigh-Ritz型方法（CIRR方法）。在该方法中，数值积分沿着一个圆，其中包含相对较少的特征值的数量来构造一个子空间。由于推导子空间的过程可以并行执行，因此所提出的方法适用于主从编程模型。数值实验验证了该方法的有效性。
We consider a Rayleigh-Ritz type eigensolver for finding a limited set of eigenvalues and their corresponding eigenvectors in a certain region of generalized eigen- value problems. When the matrices are very large, iterative methods are used to generate an invariant subspace that contains the desired eigenvectors. Approximations are ex- tracted from the subspace through a Rayleigh-Ritz projection. In this paper, we present a Rayleigh-Ritz type method with a contour integral (CIRR method). In this method, numerical integration along a circle that contains relatively small number of eigenval- ues is used to construct a subspace. Since the process to derive the subspace can be performed in parallel, the presented method is suitable for master-worker programming models. Numerical experiments illustrate the property of the proposed method.