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A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition

Hou, Thomas Y. and Huang, De and Lam, Ka Chun and Zhang, Ziyun (2019) A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition. Multiscale Modeling and Simulation, 17 (1). pp. 260-306. ISSN 1540-3459. https://resolver.caltech.edu/CaltechAUTHORS:20190416-073721627

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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 component 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1137/18m1180827DOIArticle
https://arxiv.org/abs/1804.03415arXivDiscussion Paper
Additional Information:© 2019 Society for Industrial and Applied Mathematics. Received by the editors April 16, 2018; accepted for publication (in revised form) December 3, 2018; published electronically January 30, 2019. This research was supported in part by the NSF grants DMS-1318377 and DMS-1613861.
Funders:
Funding AgencyGrant Number
NSFDMS-1318377
NSFDMS-1613861
Subject Keywords:leftmost eigenpairs, sparse symmetric positive definite, multiresolution matrix decomposition, implicitly restarted Lanczos method, preconditioned conjugate gradient method, eigenpair refinement
Issue or Number:1
Classification Code:AMS subject classifications. 15A18, 15A12, 65F08, 65F15
Record Number:CaltechAUTHORS:20190416-073721627
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190416-073721627
Official Citation:A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition Thomas Y. Hou, De Huang, Ka Chun Lam, and Ziyun Zhang Multiscale Modeling & Simulation 2019 17:1, 260-306; doi: 10.1137/18m1180827
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94725
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Apr 2019 21:29
Last Modified:03 Oct 2019 21:06

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