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.