Continued fractions and linear recurrences
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- by W. H. Mills PDF
- Math. Comp. 29 (1975), 173-180 Request permission
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 \[ \sum \limits _{j = 0}^s {{t_{i + j}}{\lambda _j},\quad 0 \leqslant i \leqslant s - 1,} \] for every positive integer s.References
- 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
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 173-180
- MSC: Primary 10F45
- DOI: https://doi.org/10.1090/S0025-5718-1975-0369276-7
- MathSciNet review: 0369276