Logic Programming Applied to Numerical Integration.

Abstract

This paper uses logic programming to describe numerical integration in a general way. Axioms are added to the basic logic programs to define specific known numerical integration algorithms. Using a slightly different formalization, we construct logic programs for adaptive Romberg integration and for a new algorithm for adaptive integration. The logic programs provide a formal basis for classifying numerical quadrature algorithms (recall Rice's comment that there are 1,000,000 useful ones). The logic programs are also more understandable than the corresponding programs in conventional programming languages. In terms of logic programming there are several novel points in this paper. The data type, real number, is not definded by a recursive constructor function. Termination is decided by error bounds, rather than by reaching some basis case of the data constructor. The problem itself seems to demand concurrent execution and global variables but in fact is solved in a linear fashion. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1978
Accession Number
ADA058581

Entities

People

  • Keith Clark
  • Sharon Sickel
  • W. M. Mckeeman

Organizations

  • University of California, Santa Cruz

Tags

Communities of Interest

  • C4I
  • Counter IED
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Calculus
  • Computations
  • Computer Programming
  • Computer Science
  • Efficiency
  • Information Science
  • Integrals
  • Language
  • Mathematics
  • Military Research
  • Numbers
  • Numerical Analysis
  • Numerical Integration
  • Numerical Quadrature
  • Real Numbers
  • Specifications

Fields of Study

  • Engineering

Readers

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