# Accession Number:

## AD0673674

# Title:

## EPSILON-CALCULUS.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## STANFORD UNIV CALIF DEPT OF COMPUTER SCIENCE

# Personal Author(s):

# Report Date:

## 1968-08-16

# Pagination or Media Count:

## 147.0

# 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:

# Subject Categories:

- Theoretical Mathematics
- Computer Programming and Software