Reflections on value regions, limit regions and truncation errors for continued fractions

Rye, Egil; Waadeland, Haakon

doi:10.1007/bf01389709

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1986

1989

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Cited by 9 publications

(2 citation statements)

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“…Actually it is the best limit region, since it is the smallest one. For a definition of limit region see for instance [1] or [4]. By letting p~0, it is easy to see, that (0, q] is a convergence region, and (0, q] is the corresponding best limit region.…”

Section: The Problemmentioning

confidence: 98%

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Some observations on the distribution of values of continued fractions

1989

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Summary. There have been many studies of the values taken on by continued fractions K(a./1) when its elements are all in a prescribed set E. The set of all values taken on is the limit region V(E). It has been conjectured that the values in V(E) are taken on with varying probabilities even when the elements a. are uniformly distributed over E. In this article we present the first concrete evidence that this is indeed so. We consider two types of element regions: (A) E is an interval on the real axis. Our best results are for intervals [-p(1--p), p(1--p)], 0

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Section: The Problemmentioning

confidence: 98%

“…Such knowledge is useful for several purposes, e.g. for finding a priori truncation error estimates, see for instance [3] and [4], including references cited there. If in particular E is such that ( a.e [p,q] for all n, then fe IX, Y].…”

Section: The Problemmentioning

confidence: 99%