# Accession Number:

## ADA014059

# Title:

## Multiple-Precision Zero-Finding Methods and the Complexity of Elementary Function Evaluation

# Descriptive Note:

## Interim rept.

# Corporate Author:

## CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE

# Personal Author(s):

# Report Date:

## 1975-07-01

# Pagination or Media Count:

## 29.0

# Abstract:

The author considers methods for finding high-precision approximations to simple zeros of smooth functions. As an application, the author gives fast methods for evaluating the elementary functions logx, expx , sinx etc. to high precision. For example, if x is a positive floating-point number with an n-bit fraction, then under rather weak assumptions an n-bit approximation to logx or expx may be computed in time asymptotically equal to 13Mn log of n to the base 2 as n approaches infinity, where Mn is the time required to multiply floating-point numbers with n-bit fractions. Similar results are given for the other elementary functions, and some analogies with operations on formal power series are mentioned.

# Subject Categories:

- Numerical Mathematics