In mathematics, the Jacobi–Perron algorithm is a generalization of the Euclidean algorithm to n-tuples of real numbers, which addresses Hermite's problem.[1] It was defined by C. G. J. Jacobi for n = 2 and Oskar Perron for n ≥ 2.[2]
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Bernstein: The modified algorithm of Jacobi-Perron. Memoirs of the AMS 67, Providence, 1966 Leon Bernstein: The Jacobi-Perron algorithm - its theory and application
Jacobi–Perron algorithm Jacobi−Trudi identities Jacobi conformal projections Jacobi coordinates Jacobi eigenvalue algorithm Jacobi ellipsoid Jacobi elliptic
Euclidean algorithm function. Euclidean rhythm, a method for using the Euclidean algorithm to generate musical rhythms Jacobi–Perron algorithm, a generalization
cubic vectors) and all dimensions d ≥ 3 {\displaystyle d\geq 3} . Jacobi–Perron algorithm Euler, Leonhard (1748), Introductio in analysin infinitorum, Vol
is an alternate approach to the Hermite problem (of which the Jacobi-Perron algorithm is yet another approach). For the case of ordered pairs, if the
found on pp. 170–176. They cite two sources of the proofs at Landau 1927 or Perron 1910; see the "List of Books" at pp. 417–419 for full citations. Oughtred
Learning as well. It is the left-adjoint of the transfer operator of Frobenius–Perron. Using the language of category theory, the composition operator is a pull-back
Aesthetic Aspects of Analysis. Springer. p. 589. ISBN 978-1-4939-6793-3. Perron, Oskar (1957). Die Lehre von den Kettenbrüchen: Band II (in German) (Third ed
