Performance and Accuracy of LAPACK's Symmetric TridiagonalEigensolvers

PDF Version Also Available for Download.

Description

We compare four algorithms from the latest LAPACK 3.1 release for computing eigenpairs of a symmetric tridiagonal matrix. These include QR iteration, bisection and inverse iteration (BI), the Divide-and-Conquer method (DC), and the method of Multiple Relatively Robust Representations (MR). Our evaluation considers speed and accuracy when computing all eigenpairs, and additionally subset computations. Using a variety of carefully selected test problems, our study includes a variety of today's computer architectures. Our conclusions can be summarized as follows. (1) DC and MR are generally much faster than QR and BI on large matrices. (2) MR almost always does the fewest ... continued below

Creation Information

Demmel, Jim W.; Marques, Osni A.; Parlett, Beresford N. & Vomel,Christof April 19, 2007.

Context

This article 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. More information about this article can be viewed below.

Who

People and organizations associated with either the creation of this article or its content.

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this article. Follow the links below to find similar items on the Digital Library.

Description

We compare four algorithms from the latest LAPACK 3.1 release for computing eigenpairs of a symmetric tridiagonal matrix. These include QR iteration, bisection and inverse iteration (BI), the Divide-and-Conquer method (DC), and the method of Multiple Relatively Robust Representations (MR). Our evaluation considers speed and accuracy when computing all eigenpairs, and additionally subset computations. Using a variety of carefully selected test problems, our study includes a variety of today's computer architectures. Our conclusions can be summarized as follows. (1) DC and MR are generally much faster than QR and BI on large matrices. (2) MR almost always does the fewest floating point operations, but at a lower MFlop rate than all the other algorithms. (3) The exact performance of MR and DC strongly depends on the matrix at hand. (4) DC and QR are the most accurate algorithms with observed accuracy O({radical}ne). The accuracy of BI and MR is generally O(ne). (5) MR is preferable to BI for subset computations.

Source

  • Journal Name: SIAM Journal on Scientific Computing; Journal Volume: 30; Journal Issue: 3; Related Information: Journal Publication Date: 04/2008

Language

Item Type

Identifier

Unique identifying numbers for this article in the Digital Library or other systems.

  • Report No.: LBNL--62584
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 928868
  • Archival Resource Key: ark:/67531/metadc897405

Collections

This article is part of the following collection of related materials.

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.

What responsibilities do I have when using this article?

When

Dates and time periods associated with this article.

Creation Date

  • April 19, 2007

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

Usage Statistics

When was this article last used?

Yesterday: 0
Past 30 days: 1
Total Uses: 7

Interact With This Article

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

Demmel, Jim W.; Marques, Osni A.; Parlett, Beresford N. & Vomel,Christof. Performance and Accuracy of LAPACK's Symmetric TridiagonalEigensolvers, article, April 19, 2007; United States. (digital.library.unt.edu/ark:/67531/metadc897405/: accessed July 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.