Approximate Complexity and Functional Representation.

Abstract

Results are obtained dealing with the exact and the approximate representation of a function F as a superposition, in designated formats, of functions of fewer variables. Two main cases are considered. In the classical nomographic case one seeks criteria for deciding if a function can be expressed in the form f(phi(x) + psi(y)), or as a uniform limit of such functions. The second case is also related to the solution of Hilbert's 13th problem, and deals with the format F(x) = f(phi(x)) where x lies in an n-cell I and phi is a real valued continuous function on I, and f is a function on R taking values in a chosen normed space epsilon. The use of these criteria is illustrated with several specific functions.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1976
Accession Number
ADA031972

Entities

People

  • R. C. Buck

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I
  • Counter IED

DTIC Thesaurus Topics

  • Construction
  • Differential Equations
  • Dispersions
  • Equations
  • Intervals
  • Mathematics
  • Military Research
  • Monotone Functions
  • North Carolina
  • Numbers
  • Partial Differential Equations
  • Polynomials
  • Real Numbers
  • Sequences
  • Two Dimensional
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis

Technology Areas

  • Space