COLLECTIVELY COMPACT OPERATOR APPROXIMATIONS. LECTURES PRESENTED JULY-AUGUST 1967.

Abstract

A general approximation theory for linear and nonlinear operators on Banach spaces is presented. It is applied to numerical integration approximations of integral operators. Convergence of the operator approximations is pointwise rather than uniform on bounded sets, which is assumed in other theories. The operator perturbations form a collectively compact set, i.e., they map each bounded set into a single compact set. In the nonlinear case, Frechet differentiability conditions are also imposed. Principal results include convergence and error bounds for approximate solutions and, for linear operators, results on spectral approximations. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 17, 1967
Accession Number
AD0657450

Entities

People

  • Lyle Smith
  • P. M. Anselone

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Banach Space
  • Convergence
  • Integrals
  • Mathematical Analysis
  • Mathematics
  • Numerical Integration
  • Perturbations

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Mathematical Modeling and Probability Theory.
  • Theoretical Analysis.

Technology Areas

  • Space