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Selenius, C. -- Konstruktion und Theorie halbregelmassiger Kettenbruche mit idealer relativer Approximation, Acta Acad. Aboensis Math. et Phys., XXII.2 (1960), 1-75.

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A Gauss-Kusmin Theorem for Optimal Continued Fractions - Karma Dajani And   (Correct)

....does not provide closest expansions, and closest expansions (like Minkowski s diagonal continued fraction (DCF) do not provide fastest expansions, a natural question arises whether exist a SRCF which is both fastest and closest. In [Ke] it was shown that such an algorithm does exist, and Selenius [Se] showed how such a SRCF of can be obtained, given the RCF of . In 1987, W. Bosma introduced a new continued fraction expansion which yields for every 2 R a SRCF expansion of which is both fastest and closest, without using the RCF expansion of . This new continued fraction algorithm, the ....

Selenius, C. -- Konstruktion und Theorie halbregelmassiger Kettenbruche mit idealer relativer Approximation, Acta Acad. Aboensis Math. et Phys., XXII.2 (1960), 1-75.


A Gauss-Kusmin Theorem for Optimal Continued Fractions - Dajani, Kraaikamp   (Correct)

....does not provide closest expansions, and closest expansions (like Minkowski s diagonal continued fraction (DCF) do not provide fastest expansions, a natural question arises whether exist a SRCF which is both fastest and closest. In [Ke] it was shown that such an algorithm does exist, and Selenius [Se] showed how such a SRCF of can be obtained, given the RCF of . In 1987, W. Bosma introduced a new continued fraction expansion which yields for every 2 R a SRCF expansion of which is both fastest and closest, without using the RCF expansion of . This new continued fraction algorithm, the ....

Selenius, C. -- Konstruktion und Theorie halbregelmassiger Kettenbruche mit idealer relativer Approximation, Acta Acad. Aboensis Math. et Phys., XXII.2 (1960), 1-75.

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