Estimating Condition Numbers -- an Empirical Study.

Abstract

This paper investigates two proposed methods for estimating the condition number of a matrix from factorizations commonly used to solve linear systems. One method estimates the condition number with respect to the 1-norm from the LU factorization, and the other the condition number with respect to the 2-norm from the QR factorization. Random matrices of various orders having known distributions of singular values were generated and the estimated condition numbers compared with the true ones. For the classes of matrices tested in this study, the estimators performed rather well, never underestimating the condition number by a factor of more than ten. The paper also gives an efficient method for generating random orthogonal matrices with the Haar distribution. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1978
Accession Number
ADA063864

Entities

People

  • Gilbert W. Stewart

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Computational Science
  • Computations
  • Computer Science
  • Estimators
  • Histograms
  • Linear Systems
  • Maryland
  • Military Research
  • New York
  • Numbers
  • Permutations
  • Real Numbers
  • Theorems
  • Universities

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Linear Algebra