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.
|Number of pages||11|
|Publication status||Published - 2002|
- Brun's algorithm
- Jacobi-Perron algorithm
- Lyapunov exponents
- Multidimensional continued fractions
- Strong convergence