INTERVAL ARITHMETIC WITH SOME APPLICATIONS FOR DIGITAL COMPUTERS,

Abstract

The purpose of this paper is to present a proposed solution to the problem of finding rigorous error bounds, by the use of interval arithmetic. Interval arithmetic is a method of computation in which the rational operations on real numbers are replaced by corresponding operations on closed intervals. That such a replacement is always possible is shown. A discussion is given of interval arithmetic as a system - definitions, operations, theorems, and elementary consequences. An algorithm is presented for the computation of certain functions by the Taylor series, and which has error bounds built into the algorithm. Finally, closed intervals are employed to solve the initial-value first-order differential equation dy dx = f(x,y).

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1965
Accession Number
AD0618050

Entities

People

  • Sidney Shayer

Organizations

  • Lockheed Martin Missiles and Space

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Computations
  • Computers
  • Differential Equations
  • Digital Computers
  • Equations
  • Intervals
  • Mathematical Analysis
  • Mathematics
  • Real Numbers

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Computer Programming and Software Development.