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