On Machine Precision, Computation Error and Condition Number in Solving Linear Algebraic Systems.

Abstract

The relationship among the machine precision, computation error and condition number in solving linear algebraic systems is derived for floating elimination method by using backward error analysis. It is shown that the negative of the logarithm of the relative error is proportional to the machine precision for fixed system and to the negative of the logarithm of the condition of the system for fixed t. It is also shown that for fixed relative error, the machine precision required to achieve this is proportional to the logarithm of the condition of the system. Numerical experiments have been carried out and the observed data do coincide with what was expected. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1970
Accession Number
AD0714598

Entities

People

  • Franklin F. Kuo
  • Nai-kuan Tsao

Organizations

  • University of HawaiĘ»i System

Tags

DTIC Thesaurus Topics

  • Computations
  • Elimination
  • Error Analysis
  • Errors
  • Precision

Fields of Study

  • Mathematics

Readers

  • Inertial Navigation Systems.
  • Mathematical Modeling and Probability Theory.