143 research outputs found

    The rhetoric of "fairness" in Japanese and American society

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    Random Thoughts on Modern Korea History : Reflections on Three Decades of Research

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    Japan through English

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    A greedy algorithm for computing eigenvalues of a symmetric matrix

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    We present a greedy algorithm for computing selected eigenpairs of a large sparse matrix HH that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its components have large magnitudes, the proposed algorithm identifies the location of these components in a greedy manner, and obtains approximations to the desired eigenpairs of HH by computing eigenpairs of a submatrix extracted from the corresponding rows and columns of HH. Even when the eigenvector is not completely localized, the approximate eigenvectors obtained by the greedy algorithm can be used as good starting guesses to accelerate the convergence of an iterative eigensolver applied to HH. We discuss a few possibilities for selecting important rows and columns of HH and techniques for constructing good initial guesses for an iterative eigensolver using the approximate eigenvectors returned from the greedy algorithm. We demonstrate the effectiveness of this approach with examples from nuclear quantum many-body calculations, many-body localization studies of quantum spin chains and road network analysis.Comment: 19 pages, 9 figures, 1 tabl
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