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      A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition

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          Abstract

          In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multiresolution operator compression framework. We exploit the well-conditioned property of every decomposition components by integrating the multiresolution framework into the Implicitly restarted Lanczos method. We achieve this combination by proposing an extension-refinement iterative scheme, in which the intrinsic idea is to decompose the target spectrum into several segments such that the corresponding eigenproblem in each segment is well-conditioned. Theoretical analysis and numerical illustration are also reported to illustrate the efficiency and effectiveness of this algorithm.

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          Author and article information

          Journal
          10 April 2018
          Article
          1804.03415
          5cc6d3cc-cb82-4d42-b596-ed3261744e6b

          http://creativecommons.org/licenses/by-nc-sa/4.0/

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          Custom metadata
          46 pages, 11 figures, 10 tables
          math.NA cs.CV

          Computer vision & Pattern recognition,Numerical & Computational mathematics

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