Description Usage Arguments Details Value Note Author(s) References See Also Examples
Partial convergents of continued fractions or generalized continued fractions
1 2 | convergents(a)
gconvergents(a,b, b0 = 0)
|
a,b |
In function |
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”
1 2 3 4 5 6 7 | # Successive approximations to pi:
jj <- convergents(c(3,7,15,1,292))
jj$A/jj$B - pi # should get smaller
convergents(rep(1,10))
|
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