Rank Revealing QR-Factorizations.

Abstract

An algorithm is presented for computing a column permutation Pi and a QR-factorization (A)(Pi) = QR of an m by n (m > or = n) matrix A such that a possible rank deficiency of A will be revealed in the triangular factor R having a small lower right block. For low rank deficient matrices, the algorithm is guaranteed to reveal the rank of A and the cost is only slightly more than the cost of one regular QR-factorization. A posteriori upper and lower bounds on the singular values of A are derived and can be used to infer the numerical rank of A. Keywords: QR-Factorization; Rank deficient matrices; Least squares computation; Subset selection; Rank; Singular values.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1985
Accession Number
ADA156756

Entities

People

  • T. F. Chan

Organizations

  • Yale University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Computations
  • Computer Science
  • Computers
  • Contracts
  • Decomposition
  • Deficiencies
  • Estimators
  • Iterations
  • Military Research
  • Notation
  • Optimal Estimators
  • Permutations
  • Precision
  • Rotation
  • Universities

Fields of Study

  • Engineering

Readers

  • Approximation Theory.
  • Astronomy/Astrophysics
  • Regression Analysis.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms