A Convergence Theorem for Newton's Method in Banach Spaces.

Abstract

To find sharper error bounds for iterative solution of nonlinear equations under assumptions as weak as possible is of basic importance in numerical analysis. This paper gives a convergence theorem for Newton's method in Banach spaces which improves the theorems of Kantorovich, Lancaster and Ostrowski. The error bounds obtained improve the recent results of Potra.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1985
Accession Number
ADA163625

Entities

People

  • Tetsuro Yamamoto

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Approximation (Mathematics)
  • Banach Space
  • Contracts
  • Convergence
  • Convex Sets
  • Equations
  • Error Analysis
  • Functional Analysis
  • Mathematics
  • New York
  • Notation
  • Numerical Analysis
  • Sequences
  • Theorems
  • United States
  • Universities
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Linear Algebra

Technology Areas

  • Space