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Continued fractions

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  • Décio Luiz Gazzoni Filho
    If I m given a fraction x/y = a_0 + 1/(a_1 + 1/(a_2 + ... + 1/(a_n)...)), what is the fastest way to compute w/z = a_0 + 1/(a_1 + 1/(a_2 + ... +
    Message 1 of 1 , Jan 7, 2005
      If I'm given a fraction x/y = a_0 + 1/(a_1 + 1/(a_2 + ... + 1/(a_n)...)), what
      is the fastest way to compute w/z = a_0 + 1/(a_1 + 1/(a_2 + ... +
      1/(a_{n-1})...))? Basically I want the best approximation to x/y involving
      slightly smaller numerators and denominators. Assume that the continued
      fraction expansion of x/y isn't known a priori; I'm trying to figure out if
      it is possible to avoid computing this continued fraction expansion, as the
      computation is fairly expensive.

      Décio


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