What do continued fractions accomplish?

DOI10.1007/s00591-006-0003-xzbMath1171.11302OpenAlexW2015945920MaRDI QIDQ2457887

Fritz Schweiger

Publication date: 23 October 2007

Published in: Mathematische Semesterberichte (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00591-006-0003-x

zbMATH Keywords

Jacobi-Perron algorithm

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Continued fractions (11A55) Simultaneous homogeneous approximation, linear forms (11J13)

Related Items (2)

Using the Inhomogeneous Simultaneous Approximation Problem for Cryptographic Design ⋮ A two-dimensional continued fraction algorithm with Lagrange and Dirichlet properties

Cites Work

• The quality of the diophantine approximations found by the Jacobi--Perron algorithm and related algorithms
• Euclidean algorithms are Gaussian
• The Jacobi-Perron algorithm its theory and application
• A Kuzmin-type theorem with exponential convergence for a class of fibred systems
• On invariant measures of the Euclidean algorithm
• Generalizing the Continued Fraction Algorithm to Arbitrary Dimensions
• Thed-Dimensional Gauss Transformation: Strong Convergence and Lyapunov Exponents
• The Three-Dimensional Gauss Algorithm Is Strongly Convergent Almost Everywhere
• Exposants caractéristiques de l'algorithme de Jacobi-Perron et de la transformation associée. (Characteristic exponents of the Jacobi-Perron algorithm and of the associated map)
• The quality of approximation of Brun's algorithm in three dimensions
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