TRLAN User Guide

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Description

TRLAN is a program designed to find a small number of extreme eigenvalues and their corresponding eigenvectors of a real symmetric matrix. Denote the matrix as A, the eigenvalue as {lambda}, and the corresponding eigenvector as x, they are defined by the following equation, Ax = {lambda}x. There are a number of different implementations of the Lanczos algorithm available. Why another one? Our main motivation is to develop a specialized version that only target the case where one wants both eigenvalues and eigenvectors of a large real symmetric eigenvalue problems that can not use the shift-and-invert scheme. In this case ... continued below

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34 p.

Creation Information

Wu, Kesheng & Simon, H. March 9, 1999.

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This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 31 times . More information about this report can be viewed below.

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Description

TRLAN is a program designed to find a small number of extreme eigenvalues and their corresponding eigenvectors of a real symmetric matrix. Denote the matrix as A, the eigenvalue as {lambda}, and the corresponding eigenvector as x, they are defined by the following equation, Ax = {lambda}x. There are a number of different implementations of the Lanczos algorithm available. Why another one? Our main motivation is to develop a specialized version that only target the case where one wants both eigenvalues and eigenvectors of a large real symmetric eigenvalue problems that can not use the shift-and-invert scheme. In this case the standard non-restarted Lanczos algorithm requires one to store a large number of Lanczos vectors which can cause storage problem and make each iteration of the method very expensive. The underlying algorithm of TRLAN is a dynamic thick-restart Lanczos algorithm. Like all restarted methods, the user can choose how many vectors can be generated at once. Typically, th e user chooses a moderate size so that all Lanczos vectors can be stored in core. This allows the restarted methods to execute efficiently. This implementation of the thick-restart Lanczos method also uses the latest restarting technique, it is very effective in reducing the time required to compute a desired solutions compared to similar restarted Lanczos schemes, e.g., ARPACK.

Physical Description

34 p.

Notes

OSTI as DE00006539

Medium: P; Size: 34 pages

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  • Other Information: Supercedes report DE00006539; PBD: 9 Mar 1999

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  • Report No.: LBNL--42953
  • Grant Number: AC03-76SF00098
  • DOI: 10.2172/6539 | External Link
  • Office of Scientific & Technical Information Report Number: 6539
  • Archival Resource Key: ark:/67531/metadc703105

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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Creation Date

  • March 9, 1999

Added to The UNT Digital Library

  • Sept. 12, 2015, 6:31 a.m.

Description Last Updated

  • April 12, 2017, 1:43 p.m.

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Wu, Kesheng & Simon, H. TRLAN User Guide, report, March 9, 1999; California. (digital.library.unt.edu/ark:/67531/metadc703105/: accessed October 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.