A linear algorithm for nonhomogeneous spectra of numbers |
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Authors: | M Boshernitzan A.S Fraenkel |
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Affiliation: | 1. Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel 76100;3. Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel 76100 |
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Abstract: | Given a sequence of integers [ai]i=1n, an O(n) iterative algorithm is presented which decides whether there exist real numbers α and β such that ai = [iα + β] (1 ? i ? n). In fact, the linear algorithm computes the partial quotients of the continued fraction expansions of and such that if and only if ai = [iα + β] (1 ? i ? n) for suitable β = β(α). |
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