Accession Number : AD0673674

Title :   EPSILON-CALCULUS.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF COMPUTER SCIENCE

Personal Author(s) : Richman,Paul L.

Report Date : 16 AUG 1968

Pagination or Media Count : 147

Abstract : Recursive function theory is used to lay the basis for a partially constructive theory of calculus, which we call the epsilon-calculus. This theory differs from other theories that have grown out of recursive function theory in that (1) it is directly related to the variable-precision computations used in scientific computation today, and (2) it deals explicitly with intermediate results rather than ideal answers. As epsilon approaches zero, intermediate results in the epsilon-calculus approach their corresponding answers in the calculus. Thus we say 'the epsilon-calculus approaches the calculus, as epsilon approaches zero.' It is hoped that investigations in the epsilon-calculus will lead to a better understanding of numerical analysis. Several new results in this direction are presented, concerning instability and also machine numbers. Discrete notions of limit, convergence, continuity, arithmetic, derivative and integral are also presented and analyzed. (Author)

Descriptors :   (*MATHEMATICAL LOGIC, *NUMERICAL ANALYSIS), RECURSIVE FUNCTIONS, COMPUTER PROGRAMMING, APPROXIMATION(MATHEMATICS), FUNCTIONAL ANALYSIS, SET THEORY, THESES

Subject Categories : Theoretical Mathematics
      Computer Programming and Software

Distribution Statement : APPROVED FOR PUBLIC RELEASE