A generalization of the simple continued fraction algorithm
Theresa P. Vaughan
Math. Comp. 32 (1978), 537-558
Primary 10F20; Secondary 10A30
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Abstract: In this paper we present a generalization of the continued fraction algorithm, based on a geometric and matrix-theoretic approach.
We first give a geometric representation in the plane , of the simple continued fraction algorithm, described in terms of geometric and arithmetic properties of matrices with nonnegative integer entries and determinant 1. The algorithm of this paper is then derived as a natural generalization of the situation in . We describe a computational procedure for our algorithm, and give several examples.
Bernstein, The Jacobi-Perron algorithm—Its theory and
application, Lecture Notes in Mathematics, Vol. 207, Springer-Verlag,
Berlin-New York, 1971. MR 0285478
C. D. OLDS, Continued Fractions, Math. Assoc. Amer., New Mathematical Library, 1963.
HARRIS HANCOCK, Development of the Minkowski Geometry of Numbers, Dover, New York, 1964.
- LEON BERNSTEIN, The Jacobi-Perron Algorithm: Its Theory and Application, Lecture Notes in Math., vol. 207, Springer-Verlag, Berlin and New York, 1971. MR 0285478 (44:2696)
- C. D. OLDS, Continued Fractions, Math. Assoc. Amer., New Mathematical Library, 1963.
- HARRIS HANCOCK, Development of the Minkowski Geometry of Numbers, Dover, New York, 1964.
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