research-article

Adaptive Projection Subspace Dimension for the Thick-Restart Lanczos Method

Authors:

Ichitaro Yamazaki,

Kesheng WuAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 37, Issue 3

Article No.: 27, Pages 1 - 18

https://doi.org/10.1145/1824801.1824805

Published: 01 September 2010 Publication History

Abstract

The Thick-Restart Lanczos (TRLan) method is an effective method for solving large-scale Hermitian eigenvalue problems. The performance of the method strongly depends on the dimension of the projection subspace used at each restart. In this article, we propose an objective function to quantify the effectiveness of the selection of subspace dimension, and then introduce an adaptive scheme to dynamically select the dimension to optimize the performance. We have developed an open-source software package a--TRLan to include this adaptive scheme in the TRLan method. When applied to calculate the electronic structure of quantum dots, a--TRLan runs up to 2.3x faster than a state-of-the-art preconditioned conjugate gradient eigensolver.

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 37, Issue 3

September 2010

296 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/1824801

Issue’s Table of Contents

Copyright © 2010 ACM.

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Association for Computing Machinery

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Publication History

Published: 01 September 2010

Accepted: 01 February 2010

Revised: 01 October 2009

Received: 01 September 2008

Published in TOMS Volume 37, Issue 3

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Cited By

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https://doi.org/10.1103/PhysRevB.110.165419
Delicado PPachón-García C(2024)Multidimensional scaling for big dataAdvances in Data Analysis and Classification10.1007/s11634-024-00591-9Online publication date: 13-Apr-2024
https://doi.org/10.1007/s11634-024-00591-9
Xu CXu WJing K(2023)Fast algorithms for singular value decomposition and the inverse of nearly low-rank matricesNational Science Review10.1093/nsr/nwad08310:6Online publication date: 25-Mar-2023
https://doi.org/10.1093/nsr/nwad083
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Aishima K(2019)Global convergence of the restarted Lanczos and Jacobi---Davidson methods for symmetric eigenvalue problemsNumerische Mathematik10.1007/s00211-015-0699-4131:3(405-423)Online publication date: 2-Jan-2019
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Huang QNishigori TKatada MFujii AKuo J(2018) Fermi resonance in solvated H 3 O + : a counter-intuitive trend confirmed via a joint experimental and theoretical investigation Physical Chemistry Chemical Physics10.1039/C8CP02151A20:20(13836-13844)Online publication date: 2018
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