Computational Implementation of the Multivariate Halley Method for Solving Nonlinear Systems of Equations.

Abstract

Halley's method for the solution of systems of equations is an iterative procedure which converges cubically under favorable conditions. The multivariate version requires the solution of two linear systems of equations with the same coefficient matrix, following which the correction vector is computed using componentwise multiplication and division of vectors. This report describes a general-purpose computer program which implements this method. The necessary first and second derivatives are obtained by automatic differentiation, so the user need only supply code defining the functions appearing in the system of equations. The program is written in Pascal-SC, using the new data type HESSIAN to represent dependent and independent variables. Numerical examples are given for two simple systems of equations to illustrate the use of the program and the effectiveness of the method.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1983
Accession Number
ADA127782

Entities

People

  • Annie A. M. Cuyt
  • Louis B. Rall

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Arithmetic
  • Automatic
  • Compilers
  • Computations
  • Computer Programming
  • Computer Programs
  • Computers
  • Iterations
  • Linear Systems
  • Mathematics
  • Nonlinear Systems
  • Operating Systems
  • Procedures (Computers)
  • Test And Evaluation
  • United States
  • Universities
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra