ROUTINE FOR IMPROVING THE ACCURACY OF THE ROOTS OF POLYNOMIALS WITH REAL COEFFICIENTS.

Abstract

A routine has been developed to compute the real and complex conjugate roots for a polynomial with real coefficients. When the polynomial is of odd degree, the routine locates one real root and then reduces the polynomial to an even degree. The remainder of the roots are located in pairs by using factors and Bairstow's Algorithm. There is no special provision to detect multiple roots and hence the routine may fail or converge to incorrect values. Computing roots of polynomials related to the Transient Response of a Viscoelastic Torsional Pendulum illustrated the effect that small errors in computed roots have on subsequent computations. A need arose to eliminate as many errors as possible. The routine tries to eliminate most errors in extracting roots by: scaling; using equations yielding least error; refining extracted roots, both real and imaginary, to a prescribed accuracy by the Newton-Raphson Method. Other error checks are included to achieve as much accuracy as possible. Several examples are included. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1965
Accession Number
AD0629042

Entities

People

  • Alene K. Depue

Organizations

  • Ballistic Research Laboratory

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Coefficients
  • Computations
  • Equations
  • Errors
  • Mathematical Analysis
  • Mathematics
  • Pendulums
  • Polynomials
  • Refining

Fields of Study

  • Mathematics

Readers

  • Geodesy
  • Linear Algebra
  • Systems Analysis and Design