Re: [boost] What is Lenz's algorithm? (was: Re: Rational comparison w/continued fractions)

From: John Maddock (john_at_[hidden])
Date: 2005-12-19 06:13:31

> What's this algorithm?  Is it related to the Lenz's Law for
> electromagnetic physics?  (That all I found on Google.)

No, the simplest explanation is that its a way of converting a continuous 
fraction to a real number while avoiding overflow/underflow/devide by zero.

For instance given a function F(x,y,z), there is often a continued fraction 
that expresses the result of the function exactly: we can calculate the 
constants in the fraction [a1,b1 ... aN,bN] using some well known numerical 
formula, but then we need to figure out how to convert these into a 
real-number result.  In particular you need to figure out how many terms to 
evaluate to obtain an accurate result (because the fraction goes on forever, 
albeit converging: well usually anyway!).

You can think of the continued fraction representation as a more powerful 
version of a series approximation.  It's used a lot for things like the 
incomplete Beta and Gamma functions, Bessel function etc.

Getting back to the subject I mis-spelt the name!  It's Lentz's algorithm, 
and there are very few references available, although Numerical Recipies is 
one source.

Anyway, this is probably getting you sidetracked, numerical evaluation of 
continued fractions isn't really related to the manipulation of rationals, 
which is where we started :-)

John.