Error Bounds for Newton-Like Methods Under Kantorovich Type Assumptions.

Abstract

To find sharper error bounds for iterative solutions of nonlinear equations is one of the important subjects in numerical analysis. This paper gives a method to derive new a posteriori error bounds for Newton-like methods in a Banach space under Kantorovich type assumptions. The bounds found are sharper than those of Miel and include those recently obtained by Moret. The applicability of the author's method is studied for other types of iterations. Various error bounds for the Newton method under the Kantorovich assumptions are surveyed in the Appendix. Keywords: Estimates; Operators(Mathematics); Convergence.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1985
Accession Number
ADA160994

Entities

People

  • Tetsuro Yamamoto

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Banach Space
  • Contracts
  • Convergence
  • Convex Sets
  • Equations
  • Functional Analysis
  • Inequalities
  • Iterations
  • Mathematics
  • New York
  • Nonlinear Algebraic Equations
  • Notation
  • Numerical Analysis
  • Sequences
  • Two Dimensional
  • United States
  • Universities

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space