Category:Continued Fraction Algorithm

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This category contains pages concerning Continued Fraction Algorithm:


The Continued Fraction Algorithm is a method for finding the continued fraction expansion for any irrational number to as many partial denominators as desired.


Let $x_0$ be the irrational number in question.

The steps are:

\(\text {(1)}: \quad\) \(\ds k\) \(=\) \(\ds 0\) initialise
\(\text {(2)}: \quad\) \(\ds a_k\) \(=\) \(\ds \floor {x_k}\) the $k$th partial denominator (that is, $a_k$) is the integer part of $x_k$
\(\text {(3)}: \quad\) \(\ds x_{k + 1}\) \(=\) \(\ds \frac 1 {x_k - a_k}\) the subsequent term is the reciprocal of the fractional part of $x_k$
\(\text {(4)}: \quad\) \(\ds k\) \(=\) \(\ds k + 1\) increase $k$ by $1$ then go to step $(2)$


Then $x_0 = \sqbrk {a_0, a_1, a_2, \ldots}$ is the required continued fraction expansion.

Pages in category "Continued Fraction Algorithm"

The following 4 pages are in this category, out of 4 total.