A New and Efficient Program for Finding all Polynomial Roots

Abstract

Finding polynomial roots rapidly and accurately is an important problem in many areas of signal processing. We present a new program which is a combination of Muller's and Newton's method. We use the former for computing a root of the deflated polynomial which is a good estimate for the root of the original polynomial. This estimate is improved by applying Newton's method to the original polynomial. Furthermore we give a simple approach to improve the accuracy for spectral factorization in the case there are double roots on the unit circle. Finally we briefly consider the inverse problem of root finding, i.e. computing the polynomial coefficients from the roots which may lead to surprisingly large numerical errors.

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Document Details

Document Type
Technical Report
Publication Date
Apr 15, 1994
Accession Number
ADA631175

Entities

People

  • Bernhard-christian Frenzel
  • Markus Lang

Organizations

  • Rice University

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Computer Science
  • Computers
  • Convergence
  • Copyrights
  • Eigenvalues
  • Engineering
  • Errors
  • Inverse Problems
  • Iterations
  • Linear Systems
  • Numerical Analysis
  • Polynomials
  • Sequences
  • Signal Processing
  • Transfer Functions

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Linear Algebra