A tight and explicit representation of Q in sparse QR factorization

PDF Version Also Available for Download.

Description

In QR factorization of a sparse m{times}n matrix A (m {ge} n) the orthogonal factor Q is often stored implicitly as a lower trapezoidal matrix H known as the Householder matrix. This paper presents a simple characterization of the row structure of Q, which could be used as the basis for a sparse data structure that can store Q explicitly. The new characterization is a simple extension of a well known row-oriented characterization of the structure of H. Hare, Johnson, Olesky, and van den Driessche have recently provided a complete sparsity analysis of the QR factorization. Let U be the ... continued below

Physical Description

Pages: (33 p)

Creation Information

Ng, E.G. & Peyton, B.W. May 1, 1992.

Context

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. More information about this report can be viewed below.

Who

People and organizations associated with either the creation of this report 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 report. Follow the links below to find similar items on the Digital Library.

Description

In QR factorization of a sparse m{times}n matrix A (m {ge} n) the orthogonal factor Q is often stored implicitly as a lower trapezoidal matrix H known as the Householder matrix. This paper presents a simple characterization of the row structure of Q, which could be used as the basis for a sparse data structure that can store Q explicitly. The new characterization is a simple extension of a well known row-oriented characterization of the structure of H. Hare, Johnson, Olesky, and van den Driessche have recently provided a complete sparsity analysis of the QR factorization. Let U be the matrix consisting of the first n columns of Q. Using results from, we show that the data structures for H and U resulting from our characterizations are tight when A is a strong Hall matrix. We also show that H and the lower trapezoidal part of U have the same sparsity characterization when A is strong Hall. We then show that this characterization can be extended to any weak Hall matrix that has been permuted into block upper triangular form. Finally, we show that permuting to block triangular form never increases the fill incurred during the factorization.

Physical Description

Pages: (33 p)

Notes

OSTI; NTIS; GPO Dep.

Language

Item Type

Identifier

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

  • Other: DE92014814
  • Report No.: ORNL/TM-12059
  • Grant Number: AC05-84OR21400
  • DOI: 10.2172/5256662 | External Link
  • Office of Scientific & Technical Information Report Number: 5256662
  • Archival Resource Key: ark:/67531/metadc1072289

Collections

This report 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 report?

When

Dates and time periods associated with this report.

Creation Date

  • May 1, 1992

Added to The UNT Digital Library

  • Feb. 4, 2018, 10:51 a.m.

Description Last Updated

  • March 5, 2018, 6:08 p.m.

Usage Statistics

When was this report last used?

Yesterday: 0
Past 30 days: 1
Total Uses: 3

Interact With This Report

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

Ng, E.G. & Peyton, B.W. A tight and explicit representation of Q in sparse QR factorization, report, May 1, 1992; Tennessee. (digital.library.unt.edu/ark:/67531/metadc1072289/: accessed September 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.