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- W2080974076 abstract "For any finite setAof positive integers, letEA :={α∈(0, 1):αis irrational, and every partial quotient in the (infinite) simple continued fraction expansion ofαis an element ofA}. For setsAwith fewer than two elements,EAis uninteresting. For |A|⩾2,EAis a kind of Cantor fractal dust, with a Hausdorff dimension (dim EA) between 0 and 1. This work presents an algorithm which, given a finite setAof between 2 andNpositive integers 2N, determines dim EAto within ±2−NusingO(N7) elementary bit operations. There is also a convenient implementation of the algorithm in Mathematica® code, together with a small table and some conjectures." @default.
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- W2080974076 date "1996-05-01" @default.
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- W2080974076 title "A Polynomial Time Algorithm for the Hausdorff Dimension of Continued Fraction Cantor Sets" @default.
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- W2080974076 doi "https://doi.org/10.1006/jnth.1996.0058" @default.
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