Convergence and Complexity of Interpolatory-Newton Iteration in a Banach Space.

Abstract

The class of Interpolatory-Newton iterations is defined and analyzed for the computation of a simple zero of a non-linear operator in a Banach space of finite or infinite dimension. Convergence of the class is established. The concepts of informationally optimal class of algorithms and optimal algorithm are formalized. For the multivariate case, the optimality of Newton iteration is established in the class of one-point iterations under an equal cost assumption. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1977
Accession Number
ADA040272

Entities

People

  • H. Wozniakowski
  • Joseph F. Traub

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Banach Space
  • Computational Complexity
  • Computations
  • Computer Science
  • Computers
  • Convergence
  • Equations
  • Iterations
  • Military Research
  • New York
  • Pennsylvania
  • Polynomials
  • Quadratic Equations
  • Universities

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space