THREE-POINT HYPERBOLIC EXTRAPOLATION TO SOLVE EQUATIONS,

Abstract

Three-point parabolic extrapolation to iteratively solve real or complex, algebraic or transcendental equations has been proposed by D. E. Muller and used frequently on automatic computers, particularly in determination of eigenvalues of matrices. It is suggested that three-point equilateral hyperbolic extrapolation enjoys the same reasons for adoptions as parabolic extrapolation, but has the added advantages that one avoids at each iteration a square root determination, a sign determination, and necessity of guarding against the possibility of being thrust into the complex domain when seeking real roots of real equations. It is also shown that the order of convergence is the same as that of parabolic extrapolation. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1964
Accession Number
AD0430200

Entities

People

  • M. L. Juncosa

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Automatic
  • Computers
  • Convergence
  • Differential Equations
  • Eigenvalues
  • Equations
  • Extrapolation
  • Iterations
  • Mathematical Analysis
  • Mathematics
  • Square Roots

Readers

  • Approximation Theory.
  • Linear Algebra