Unsymmetric ordering using a constrained Markowitz scheme

PDF Version Also Available for Download.

Description

We present a family of ordering algorithms that can be used as a preprocessing step prior to performing sparse LU factorization. The ordering algorithms simultaneously achieve the objectives of selecting numerically good pivots and preserving the sparsity. We describe the algorithmic properties and challenges in their implementation. By mixing the two objectives we show that we can reduce the amount of fill-in in the factors and reduce the number of numerical problems during factorization. On a set of large unsymmetric real problems, we obtained the median reductions of 12% in the factorization time, of 13% in the size of the ... continued below

Creation Information

Amestoy, Patrick R.; S., Xiaoye & Pralet, Stephane January 18, 2005.

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.

Sponsor

Publisher

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 present a family of ordering algorithms that can be used as a preprocessing step prior to performing sparse LU factorization. The ordering algorithms simultaneously achieve the objectives of selecting numerically good pivots and preserving the sparsity. We describe the algorithmic properties and challenges in their implementation. By mixing the two objectives we show that we can reduce the amount of fill-in in the factors and reduce the number of numerical problems during factorization. On a set of large unsymmetric real problems, we obtained the median reductions of 12% in the factorization time, of 13% in the size of the LU factors, of 20% in the number of operations performed during the factorization phase, and of 11% in the memory needed by the multifrontal solver MA41-UNS. A byproduct of this ordering strategy is an incomplete LU-factored matrix that can be used as a preconditioner in an iterative solver.

Subjects

Keywords

STI Subject Categories

Source

  • Journal Name: SIAM J. Matrix Analysis and Applications; Journal Volume: 29; Journal Issue: 1; Related Information: Journal Publication Date: 2007

Language

Item Type

Identifier

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

  • Report No.: LBNL--56861
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 920053
  • Archival Resource Key: ark:/67531/metadc894256

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

  • January 18, 2005

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

Description Last Updated

  • Sept. 22, 2017, 3:06 p.m.

Usage Statistics

When was this article last used?

Congratulations! It looks like you are the first person to view this item online.

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

Amestoy, Patrick R.; S., Xiaoye & Pralet, Stephane. Unsymmetric ordering using a constrained Markowitz scheme, article, January 18, 2005; United States. (digital.library.unt.edu/ark:/67531/metadc894256/: accessed December 12, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.