Extension of Newton's Method to Mixed Systems of Nonlinear Equations and Inequalities.

Abstract

The paper shows how Newton's method may be extended, by using linear programming, to solve mixed systems of nonlinear equations and inequalities of the form g(x) < or = 0, f(x) = 0. The number of equations and/or inequalities need not equal the number of variables, and the solutions need not be unique or isolated. An extension of the Kantorovich theorem is proved for this method; it shows, among other things, that the same quadratic rate of convergence holds for this technique as for the conventional version of Newton's method. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1971
Accession Number
AD0732054

Entities

People

  • Stephen M. Robinson

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Computer Programming
  • Convergence
  • Equations
  • Inequalities
  • Linear Programming
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)