From: israel@math.ubc.ca (Robert Israel)
Newsgroups: sci.math.symbolic,sci.math
Subject: Re: Continued Fractions
Date: 13 Nov 1998 22:44:18 GMT

In article <72i785$rck$1@lagrange.rutgers.edu>, bumby@lagrange.rutgers.edu (Richard Bumby) writes:

|> However, the book you mention may not be what the original poster was
|> looking for.  Indeed, while it is tempting to think of doing
|> calculations directly with the continued fraction expansion, there do
|> not seem to be any useful algorithms.  What continued fractions do
|> well is find rational approximations p/q within 1/q^2 of the number
|> being approximated.  Combining such good approximations by addition or
|> multiplication is likely to greatly increase the denominator and fail to
|> get any closer to the number.  Any general-purpose procedure for
|> calculating with continued fractions is likely to be "calculate first,
|> then find the continued fraction".  

For Gosper's algorithm for doing arithmetic with continued fractions, see
http://www.inwap.com/pdp10/hbaker/hakmem/cf.html

Robert Israel                                israel@math.ubc.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            
Vancouver, BC, Canada V6T 1Z2