METHODS OF SEARCH FOR SOLVING POLYNOMIAL EQUATIONS

Abstract

The problem of determining a zero of a given polynomial with guaranteed error bounds, using an amount of work that can be estimated a priori, is attacked by means of a class of algorithms based on the idea of systematic search. Lehmer's 'machine method' for solving polynomial equations is a special case. The use of the Schur-Cohn algorithm in Lehmer's method is replaced by a more general proximity test which reacts positively if applied at a point close to a zero of a polynomial. Various such tests are described, and the work involved in their use is estimated. The optimality and non-optimality of certain methods, both on a deterministic and on a probabilistic basis, are established.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1969
Accession Number
AD0698798

Entities

People

  • Peter Henrici

Organizations

  • Stanford University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Coefficients
  • Complex Numbers
  • Computations
  • Computer Science
  • Convergence
  • Coverings
  • Equations
  • Errors
  • Numbers
  • Numerical Analysis
  • Polynomials
  • Sequences
  • United States
  • United States Government
  • Work Functions

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Chemistry (specifically Chemical Fluorescence)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)