| convergents {contfrac} | R Documentation |
Partial convergents of continued fractions or generalized continued fractions
convergents(a) gconvergents(a,b, b0 = 0)
a,b |
In function convergents(), the elements of a
are the partial denominators (the first element of a is the
integer part of the continued fraction). In gconvergents()
the elements of a are the partial numerators and the elements
of b the partial denominators |
b0 |
The floor of the fraction |
Function convergents() returns partial convergents of the continued fraction
ommitted: see PDF
where a = a_0,a_1,a_2,... (note the
off-by-one issue).
Function gconvergents() returns partial convergents of the continued fraction
ommitted: see PDF
where a = a_1,a_2,...
Returns a list of two elements, A for the numerators and
B for the denominators
This classical algorithm generates very large partial numerators and denominators.
To evaluate limits, use functions CF() or GCF().
Robin K. S. Hankin
W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling 1992. Numerical recipes 3rd edition: the art of scientific computing. Cambridge University Press; section 5.2 “Evaluation of continued fractions”
# Successive approximations to pi: jj <- convergents(c(3,7,15,1,292)) jj$a/jj$B - pi convergents(rep(1,10))