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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Continued fractions and linear recurrences


Author: W. H. Mills
Journal: Math. Comp. 29 (1975), 173-180
MSC: Primary 10F45
DOI: https://doi.org/10.1090/S0025-5718-1975-0369276-7
MathSciNet review: 0369276
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Abstract: Let $ {t_0},{t_1},{t_2}, \cdots $ be a sequence of elements of a field F. We give a continued fraction algorithm for $ {t_0}x + {t_1}{x^2} + {t_2}{x^3} + \cdots $. If our sequence satisfies a linear recurrence, then the continued fraction algorithm is finite and produces this recurrence.

More generally the algorithm produces a nontrivial solution of the system

$\displaystyle \sum\limits_{j = 0}^s {{t_{i + j}}{\lambda _j},\quad 0 \leqslant i \leqslant s - 1,} $

for every positive integer s.

References [Enhancements On Off] (What's this?)

  • [1] Neal Zierler, Linear recurring sequences and error-correcting codes, Error Correcting Codes (Proc. Sympos. Math. Res. Center, Madison, Wis., 1968), Wiley, New York, 1968, pp. 47–59. MR 0249191

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1975-0369276-7
Article copyright: © Copyright 1975 American Mathematical Society

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