Rank Degeneracy and Least Squares Problems

Abstract

This paper is concerned with least squares problems when the least squares matrix A is near a matrix that is not of full rank. A definition of numerical rank is given. It is shown that under certain conditions when A has numerical rank r there is a distinguished r dimensional subspace of the column space of A that is insensitive to how it is approximated by r independent columns of A. The consequences of this fact for the least squares problem are examined. Algorithms are described for approximating the stable part of the column space of A.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1976
Accession Number
ADA032348

Entities

People

  • G. W. Stewart
  • Gene Golub
  • Virginia Klema

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Computer Science
  • Computers
  • Data Analysis
  • Decomposition
  • Equations
  • Errors
  • Military Research
  • Notation
  • Numbers
  • Observation
  • Perturbation Theory
  • Perturbations
  • Residuals
  • Square Roots
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Military Leadership and Professional Education.
  • Operations Research

Technology Areas

  • Space