### Abstract

We discuss a method of producing computer assisted proofs of almost everywhere strong convergence of the d-dimensional Gauss algorithm. This algorithm is equivalent to Brun's algorithm and to the modified Jacobi-Perron algorithm considered by Podsypanin and Schweiger. In this paper we focus on the reduction of the problem to a finite number of calculations. These calculations have been carried out for the three-dimensional algorithm and the results, which prove almost everywhere strong convergence, will be published separately.

Original language | English |
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Pages (from-to) | 119-129 |

Number of pages | 11 |

Journal | Experimental Mathematics |

Volume | 11 |

Issue number | 1 |

Publication status | Published - 2002 |

### Keywords

- Brun's algorithm
- Jacobi-Perron algorithm
- Lyapunov exponents
- Multidimensional continued fractions
- Strong convergence

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## Cite this

Hardcastle, D. M., & Khanin, K. (2002). The d-dimensional Gauss transformation: Strong convergence and Lyapunov exponents.

*Experimental Mathematics*,*11*(1), 119-129.