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arXiv · 1804.03415

A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition

Thomas Y. Hou·De Huang·Ka Chun Lam·Ziyun Zhang
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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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Thomas Y. Hou, De Huang, Ka Chun Lam, Ziyun Zhang. 2018-04-10. A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition. https://arxiv.org/abs/1804.03415

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